Selina Concise Solutions for ICSE Class 6 Mathematics Chapter 17 Idea of Speed Distance and Time

Exercise 17(A)

Question 1. A train covers 51 km in 3 hours. Calculate its speed. How far does the train go in 30 minutes?
Answer: We are given:
Distance covered = 51 km
Total time taken = 3 hours
The formula for finding the speed is:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \)
Substituting the given numbers:
\( \text{Speed} = \frac{51}{3} = 17 \text{ km/h} \)

For the next part of the question, the given time is 30 minutes. Let us convert this duration into hours:
\( \text{Time} = 30 \text{ minutes} = \frac{30}{60} \text{ h} = \frac{1}{2} \text{ h} \)
Using the speed of 17 km/h calculated above:
\( \text{Distance} = \text{Speed} \times \text{Time} \)
\( \text{Distance} = 17 \times \frac{1}{2} = 8.5 \text{ km} \)
In simple words: To find the speed, divide the total distance by the time. To find how far it went in 30 minutes, multiply that speed by half an hour.

Exam Tip: Remember to convert minutes into hours by dividing by 60 before multiplying with speed in km/h. This keeps the units consistent and avoids calculation errors.

Question 2. A motorist travelled the distance between two towns, which is 65 km, in 2 hours and 10 minutes. Find his speed in metre per minute.
Answer: The distance separating the two towns is 65 km.
The time duration is 2 hours and 10 minutes.
Let us convert the total duration into hours:
\( \text{Time taken} = 2 \text{ hours and } 10 \text{ minutes} \)
\( = 2\frac{10}{60} \text{ hours} = 2\frac{1}{6} \text{ hours} = \frac{13}{6} \text{ hours} \)
Now, calculate the speed in km/h:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{65}{\frac{13}{6}} \text{ km/h} \)
\( = \frac{65 \times 6}{13} \text{ km/h} = 30 \text{ km/h} \)
To find the speed in metres per minute, convert kilometers to metres (multiply by 1000) and hours to minutes (divide by 60):
\( \text{Speed in m/min} = \frac{30 \times 1000}{60} = 500 \text{ m/min} \)
In simple words: First, change the minutes into a fraction of an hour to find the speed in km/h. Then, convert km to metres and hours to minutes to get the final answer in metres per minute.

Exam Tip: When converting speed from km/h to m/min, multiply by 1000 and divide by 60. Write down each conversion step clearly to gain full step-wise marks.

Question 3. A train travels 700 metres in 35 seconds. What is its speed in km/h?
Answer: Here, the train covers a distance of 700 m.
The duration of travel is 35 seconds.
Let's find the speed in metres per second first:
\( \text{Speed in m/s} = \frac{\text{Distance}}{\text{Time}} \)
\( = \frac{700}{35} = 20 \text{ m/s} \)
Now, we convert this speed into kilometers per hour:
\( \text{Speed in km/h} = \frac{20 \times 60 \times 60}{1000} = 72 \text{ km/h} \)
In simple words: First, find how many metres the train goes in one second by dividing distance by time. Then, change metres per second to kilometers per hour by multiplying by 3.6 (or by multiplying by 3600 and dividing by 1000).

Exam Tip: A quick shortcut to convert speed from m/s to km/h is to multiply by \( \frac{18}{5} \) (which is \( \frac{3600}{1000} \)). Using this shortcut can save time during exams.

Question 4. A racing car covered 600 km in 3 hours 20 minutes. Find its speed in metre per second. How much distance will the car cover in 50 sec?
Answer: Total distance travelled by the racing car = 600 km
Time spent on the journey = 3 hours 20 minutes
Let's express the time solely in hours:
\( \text{Time} = 3 \text{ hours} + \frac{20}{60} \text{ hours} = 3\frac{1}{3} \text{ hours} = \frac{10}{3} \text{ hours} \)
Now, we calculate the car's speed in km/h:
\( \text{Speed in km/h} = \frac{\text{Distance}}{\text{Time}} = \frac{600}{\frac{10}{3}} \)
\( = \frac{600 \times 3}{10} = 180 \text{ km/h} \)
Next, let's change this speed into metres per second:
\( \text{Speed in m/s} = \frac{180 \times 1000}{60 \times 60} = 50 \text{ m/s} \)
To find the distance travelled in 50 seconds, we multiply this speed by the given time:
\( \text{Distance covered} = \text{Speed} \times \text{Time} \)
\( = 50 \text{ m/s} \times 50 \text{ s} = 2500 \text{ m} = 2.5 \text{ km} \)
In simple words: Find the speed in km/h first, then convert it to metres per second. Finally, multiply this speed by 50 to find the total distance covered in that time.

Exam Tip: Always make sure to state your final distance in both metres and kilometers if the number is large. Double-check your fraction conversions to avoid minor errors.

Question 5. Rohit goes 350 km in 5 hours. Find :
(i) his speed
(ii) the distance covered by Rohit in 6.2 hours
(iii) the time taken by him to cover 210 km.
Answer: Given:
Distance travelled = 350 km
Time duration = 5 hours

(i) We calculate the speed of Rohit:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{350}{5} = 70 \text{ km/h} \)

(ii) To find how far Rohit goes in 6.2 hours:
\( \text{Distance covered} = \text{Speed} \times \text{Time} \)
\( = 70 \text{ km/h} \times 6.2 \text{ h} = 434 \text{ km} \)

(iii) To find the duration required to travel 210 km:
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{210}{70} = 3 \text{ hours} \)
In simple words: First, find Rohit's speed by dividing his distance by hours. Once you have this speed, multiply it by 6.2 to get the new distance, or divide 210 by this speed to find the new time.

Exam Tip: In questions with multiple parts, the answer from part (i) is usually needed to solve parts (ii) and (iii). Ensure your first calculation is correct to avoid a chain of errors.

Question 6. A boy drives his scooter with a uniform speed of 45 km/h. Find :
(i) the distance covered by him in 1 hour 20 min.
(ii) the time taken by him to cover 108 km.
(iii) the time taken to cover 900 m.
Answer: Given:
Speed of scooter = 45 km/h

(i) The given time is 1 hour 20 minutes. Converting this to hours:
\( \text{Time} = 1 \text{ hour} + \frac{20}{60} \text{ hours} = 1\frac{1}{3} \text{ hours} = \frac{4}{3} \text{ hours} \)
Now, find the distance:
\( \text{Distance} = \text{Speed} \times \text{Time} = 45 \times \frac{4}{3} = 60 \text{ km} \)

(ii) We need to find the duration to travel a distance of 108 km:
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{108}{45} \text{ hours} \)
\( = \frac{12}{5} \text{ hours} = 2\frac{2}{5} \text{ hours} \)
Converting the fractional part to minutes:
\( \frac{2}{5} \times 60 \text{ minutes} = 24 \text{ minutes} \)
Thus, the time taken is 2 hours 24 minutes.

(iii) To cover a distance of 900 m (which is 0.9 km or \( \frac{900}{1000} \) km):
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{900 / 1000}{45} \text{ hours} \)
\( = \frac{900}{1000} \times \frac{1}{45} = \frac{1}{50} \text{ hours} \)
Let's convert this into minutes:
\( \text{Time} = \frac{1}{50} \times 60 \text{ minutes} = 1.2 \text{ minutes} \)
Since \( 0.2 \text{ minutes} = 0.2 \times 60 \text{ seconds} = 12 \text{ seconds} \), the total time taken is 1 minute 12 seconds.
In simple words: To find the distance, multiply the speed by the time in hours. To find the time, divide the distance by the speed, making sure all units (like metres to kilometers) match up first.

Exam Tip: When dealing with mixed units like minutes and seconds, convert them carefully. Remember that 0.2 minutes is equal to 12 seconds, not 20 seconds.

Question 7. I travel a distance of 10 km and come back in 2 1/2 hours. What is my speed?
Answer: Since the journey involves going and returning, the total path length is:
\( \text{Total distance} = 10 \text{ km} + 10 \text{ km} = 20 \text{ km} \)
The total time taken is \( 2\frac{1}{2} \) hours:
\( \text{Time taken} = \frac{5}{2} \text{ hours} \)
Now, we calculate the speed:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{20}{\frac{5}{2}} \)
\( = \frac{20 \times 2}{5} = 8 \text{ km/h} \)
In simple words: Since you travel to a place and come back, you must double the one-way distance to get the total distance. Then, divide this total distance by the total time.

Exam Tip: Read the question carefully. Terms like "and come back" mean the round trip distance must be used, which is twice the one-way distance.

Question 8. A man walks a distance of 5 km in 2 hours. Then he goes in a bus to a nearby town, which is 40 km, in further 2 hours. From there, he goes to his office in an autorickshaw, a distance of 5 km, in 1/2 hour. What was his average speed during the whole journey?
Answer: Let's list the details for each part of the journey:
- Distance covered by walking = 5 km in 2 hours
- Distance covered by bus = 40 km in 2 hours
- Distance covered by autorickshaw = 5 km in \( \frac{1}{2} \) hour

First, let's find the total distance:
\( \text{Total distance} = 5 \text{ km} + 40 \text{ km} + 5 \text{ km} = 50 \text{ km} \)
Next, let's find the total time taken:
\( \text{Total time} = 2 \text{ hours} + 2 \text{ hours} + \frac{1}{2} \text{ hour} = 4\frac{1}{2} \text{ hours} = \frac{9}{2} \text{ hours} \)
Now, calculate the average speed:
\( \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{50}{\frac{9}{2}} \)
\( = \frac{50 \times 2}{9} = \frac{100}{9} \text{ km/h} = 11\frac{1}{9} \text{ km/h} \)
In simple words: To find the average speed of the entire trip, add up all the individual distances and divide that by the sum of all the travel times.

Exam Tip: Average speed is calculated by dividing total distance by total time. Never find the simple average of the individual speeds, as that is a common mistake.

Question 9. Jagan went to another town such that he covered 240 km by a car going at 60 kmh-1. Then he covered 80 km by a train, going at 100 kmh-1 and the rest 200 km, he covered by a bus, going at 50 kmh-1. What was his average speed during the whole journey?
Answer: Let's analyze the three stages of Jagan's journey:
- Travel by car: Distance of 240 km at a speed of 60 km/h.
- Travel by train: Distance of 80 km at a speed of 100 km/h.
- Travel by bus: Distance of 200 km at a speed of 50 km/h.

First, calculate the total distance:
\( \text{Total distance} = 240 \text{ km} + 80 \text{ km} + 200 \text{ km} = 520 \text{ km} \)

Next, we calculate the time taken for each stage:
- Time spent in the car: \( t_1 = \frac{240}{60} = 4 \text{ hours} \)
- Time spent on the train: \( t_2 = \frac{80}{100} = \frac{4}{5} \text{ hours} \)
- Time spent on the bus: \( t_3 = \frac{200}{50} = 4 \text{ hours} \)

Now, find the total time taken:
\( \text{Total time} = 4 + \frac{4}{5} + 4 = 8\frac{4}{5} \text{ hours} = \frac{44}{5} \text{ hours} \)

Using these values, we determine the average speed:
\( \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{520}{\frac{44}{5}} \)
\( = \frac{520 \times 5}{44} = \frac{2600}{44} = \frac{650}{11} = 59\frac{1}{11} \text{ km/h} \)
In simple words: Calculate the time taken for each of the three modes of transport separately. Then, add all the distances together and divide by the total time to get the average speed.

Exam Tip: Keep the calculations in fraction form until the very last step. This avoids rounding errors and makes it easier to write the final speed as a mixed fraction.

Question 10. The speed of sound in air is about 330 ms-1. Express this speed in kmh-1. How long will the sound take to travel 99 km?
Answer: The speed of sound in air is given as 330 m/s.
First, let's convert this speed to km/h:
\( \text{Speed in km/h} = \frac{330 \times 60 \times 60}{1000} = 1188 \text{ km/h} \)

Now, we find the time taken to cover a distance of 99 km:
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{99}{1188} \text{ hours} \)
\( = \frac{1}{12} \text{ hours} \)
Converting this fraction into minutes:
\( \text{Time} = \frac{1}{12} \times 60 = 5 \text{ minutes} \)
In seconds, this is:
\( 5 \times 60 = 300 \text{ seconds} \)
In simple words: First, change the speed of sound from metres per second to kilometers per hour. Then, divide the 99 km distance by this speed to find that it takes 5 minutes (or 300 seconds).

Exam Tip: Pay close attention to arithmetic calculations. Be careful when converting speed, as a simple error in the speed conversion will affect the time calculation.

Exercise 17(B)

Question 1. A train 180 m long is running at a speed of 90 km/h. How long will it take to pass a railway signal?
Answer: We are given:
Length of the train (Distance) = 180 m
Speed of the train = 90 km/h

First, we express the time taken in hours by converting the distance to kilometers:
\( \text{Time taken} = \frac{180}{90 \times 1000} \text{ hours} = \frac{1}{500} \text{ hours} \)
Now, let's convert this time into seconds:
\( \text{Time in seconds} = \frac{1 \times 60 \times 60}{500} = \frac{36}{5} = 7.2 \text{ seconds} \)
In simple words: To pass a single point like a signal, the train has to travel its own length. Convert either the distance to km or the speed to m/s to find that it takes 7.2 seconds.

Exam Tip: When a train passes a pole, a person, or a signal, the distance covered is equal to the length of the train. Do not add any extra distance.

Question 2. A train whose length is 150 m, passes a telegraph pole in 10 sec. Find the speed of the train in km/h.
Answer: Here, the distance the train must cover to pass the pole is equal to its length:
\( \text{Distance} = 150 \text{ m} \)
The time taken to cross is 10 seconds.

First, we find the speed in metres per second:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{150}{10} = 15 \text{ m/s} \)
Now, let's convert this speed into km/h:
\( \text{Speed in km/h} = \frac{15 \times 60 \times 60}{1000} = 54 \text{ km/h} \)
In simple words: To find the speed, divide the train's length by the time it took to pass the pole. Then, convert the speed from metres per second to kilometers per hour.

Exam Tip: To convert speed from m/s to km/h quickly, multiply by \( \frac{18}{5} \). Here, \( 15 \times \frac{18}{5} = 54 \text{ km/h} \), which is a useful double-check.

Question 3. A train 120 m long passes a railway platform 160 m long in 14 sec. How long will it take to pass another platform which is 100 m long?
Answer: For the first platform:
\( \text{Total distance} = \text{Length of train} + \text{Length of platform} \)
\( = 120 \text{ m} + 160 \text{ m} = 280 \text{ m} \)
The time taken is 14 seconds.
Let's calculate the speed of the train:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{280}{14} = 20 \text{ m/s} \)

For the second platform:
\( \text{New distance to cover} = \text{Length of train} + \text{Length of second platform} \)
\( = 120 \text{ m} + 100 \text{ m} = 220 \text{ m} \)
Using the speed of 20 m/s, we find the new time required:
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{220}{20} = 11 \text{ seconds} \)
In simple words: To cross a platform, the train must cover both its own length and the platform's length. First, find the train's speed using the first platform, then use that speed to find the time needed for the second one.

Exam Tip: When crossing any platform or bridge, always add the length of the train to the length of the platform to get the total distance. Failing to do this is a very common error.

Question 4. Mr. Amit can walk 8 km in 1 hour 20 minutes.
(a) How far does he go in :
(i) 10 minutes ?
(ii) 30 seconds ?
(b) How long will it take him to walk :
(i) 2500 m ?
(ii) 6.5 km?
Answer: First, let's find Mr. Amit's walking speed:
Given distance = 8 km
Given time = 1 hour 20 minutes = \( 1 \frac{20}{60} \text{ hours} = 1 \frac{1}{3} \text{ hours} = \frac{4}{3} \text{ hours} \)
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{8}{\frac{4}{3}} = \frac{8 \times 3}{4} = 6 \text{ km/h} \)

(a) Now, we calculate the distance travelled:
(i) In 10 minutes:
Converting 10 minutes to hours: \( \frac{10}{60} \text{ hours} = \frac{1}{6} \text{ hours} \)
\( \text{Distance} = \text{Speed} \times \text{Time} = 6 \text{ km/h} \times \frac{1}{6} \text{ hours} = 1 \text{ km} \text{ (or } 1000 \text{ m)} \)
(ii) In 30 seconds:
Converting speed of 6 km/h to m/s:
\( \text{Speed} = \frac{6 \times 1000}{60 \times 60} = \frac{5}{3} \text{ m/s} \)
\( \text{Distance in 30 seconds} = \text{Speed} \times \text{Time} = \frac{5}{3} \text{ m/s} \times 30 \text{ s} = 50 \text{ m} \)

(b) Now, we calculate the time taken:
(i) To walk 2500 m:
Converting 2500 m to km: \( 2.5 \text{ km} \)
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{2.5}{6} \text{ hours} = \frac{25}{60} \text{ hours} \)
Converting to minutes:
\( \text{Time} = \frac{25}{60} \times 60 = 25 \text{ minutes} \)
(ii) To walk 6.5 km:
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{6.5}{6} \text{ hours} = \frac{65}{60} \text{ hours} \)
Converting to hours and minutes:
\( \frac{65}{60} \text{ hours} = 1 \text{ hour and } 5 \text{ minutes} \)
In simple words: First, find Amit's speed, which is 6 km/h. Use this speed to work out the distances by multiplying speed and time, and the times by dividing distance by speed.

Exam Tip: Be careful when converting units. Convert minutes or seconds to hours when working with speed in km/h, or convert the speed to m/s to make calculations simpler.

Question 5. Which is greater : a speed of 45 km/h or a speed of 12.25 m/sec?
How much is the distance travelled by each in 2 seconds?
Answer: Let's compare the two speeds:
- Speed 1 = 45 km/h
- Speed 2 = 12.25 m/s

First, let's convert Speed 2 from m/s to km/h:
\( \text{Speed 2} = \frac{12.25 \times 60 \times 60}{1000} \text{ km/h} = 44.1 \text{ km/h} \)
Comparing the two values, \( 45 \text{ km/h} > 44.1 \text{ km/h} \). Thus, the first speed of 45 km/h is greater.

Now, let's find the distance travelled by each in 2 seconds:
- Distance covered by the first speed (converting 45 km/h to m/s):
\( \text{Speed in m/s} = \frac{45 \times 1000}{3600} = 12.5 \text{ m/s} \)
\( \text{Distance} = 12.5 \text{ m/s} \times 2 \text{ s} = 25 \text{ m} \)
- Distance covered by the second speed:
\( \text{Distance} = 12.25 \text{ m/s} \times 2 \text{ s} = 24.5 \text{ m} \)
In simple words: Convert both speeds into the same unit (like km/h) to see which is faster. Then, multiply each speed in metres per second by 2 seconds to find the distance covered.

Exam Tip: To compare two physical quantities, they must be in the same units. Converting m/s to km/h is usually easier, but you can convert either way.

Question 6. A and B start from the same point and at the same time with speeds 15 km/h and 12 km/h respectively, find the distance between A and B after 6 hours if both move in :
(i) same direction
(ii) the opposite directions.
Answer: Let's find the distance each person covers in 6 hours:
- Speed of A = 15 km/h
- Speed of B = 12 km/h
Distance covered by A in 6 hours:
\( d_A = 15 \text{ km/h} \times 6 \text{ hours} = 90 \text{ km} \)
Distance covered by B in 6 hours:
\( d_B = 12 \text{ km/h} \times 6 \text{ hours} = 72 \text{ km} \)

Now, let's solve the two cases:
(i) If A and B travel in the same direction:
\( \text{Distance between them} = d_A - d_B = 90 - 72 = 18 \text{ km} \)
(ii) If A and B travel in opposite directions:
\( \text{Distance between them} = d_A + d_B = 90 + 72 = 162 \text{ km} \)
In simple words: Find the distances travelled by both A and B in 6 hours. Subtract these distances if they are going the same way, and add them if they are moving away from each other.

Exam Tip: When moving in the same direction, subtract the speeds (relative speed = 15 - 12 = 3 km/h) to find the distance (3 * 6 = 18 km). When moving in opposite directions, add the speeds.

Question 7. A and B start from the same place, in the same direction and at the same time with speeds 6 km/h and 2 m/sec respectively. After 5 hours who will be ahead and by how much?
Answer: Let's analyze the speeds and find the distances covered in 5 hours:
- Speed of A = 6 km/h
- Speed of B = 2 m/s

Distance covered by A in 5 hours:
\( d_A = 6 \text{ km/h} \times 5 \text{ h} = 30 \text{ km} \)

To find the distance covered by B, let's convert B's speed from m/s to km/h:
\( \text{Speed of B in km/h} = \frac{2 \times 60 \times 60}{1000} = 7.2 \text{ km/h} \)
Distance covered by B in 5 hours:
\( d_B = 7.2 \text{ km/h} \times 5 \text{ h} = 36 \text{ km} \)

Comparing their distances, we see that B is ahead because \( 36 \text{ km} > 30 \text{ km} \).
The difference in distance is:
\( 36 \text{ km} - 30 \text{ km} = 6 \text{ km} \)
Thus, B will be ahead by 6 km.
In simple words: Find out how far both A and B travel in 5 hours by making sure their speeds are in the same units. B goes 36 km while A goes 30 km, so B is ahead by 6 km.

Exam Tip: Be sure to convert B's speed to km/h first to make comparing the distances straightforward and to avoid large numbers in metres.

Question 8. Mohit covers a certain distance in 6 hrs by his scooter at a speed of 40 kmh-1.
(i) Find the time taken by Manjoor to cover the same distance by his car at the speed of 60 kmh-1.
(ii) Find the speed of Joseph, if he takes 8 hrs to complete the same distance.
Answer: First, let's find the total distance covered by Mohit:
Speed = 40 km/h
Time = 6 hours
\( \text{Distance} = 40 \text{ km/h} \times 6 \text{ hours} = 240 \text{ km} \)

(i) Manjoor travels this same distance of 240 km at a speed of 60 km/h:
\( \text{Time taken by Manjoor} = \frac{\text{Distance}}{\text{Speed}} = \frac{240}{60} = 4 \text{ hours} \)

(ii) Joseph takes 8 hours to cover the same 240 km:
\( \text{Speed of Joseph} = \frac{\text{Distance}}{\text{Time}} = \frac{240}{8} = 30 \text{ km/h} \)
In simple words: Find the total distance by multiplying Mohit's speed and time to get 240 km. Then, divide this distance by Manjoor's speed to find his time, and by Joseph's time to find his speed.

Exam Tip: Since the distance is constant for all three people, calculate it first. This common distance is the key to solving both parts of the question.

Question 9. A boy swims 200 m in still water and then returns back to the point of start in total 10 minutes. Find the speed of his swim in
(i) ms-1
(ii) kmh-1.
Answer: The swimmer goes 200 m and returns, so the total distance covered is:
\( \text{Total distance} = 200 \text{ m} + 200 \text{ m} = 400 \text{ m} \)
The total time taken is 10 minutes:
\( \text{Time taken} = 10 \text{ minutes} = 10 \times 60 \text{ seconds} = 600 \text{ seconds} \)

(i) Speed in m/s:
\( \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{400}{600} = \frac{2}{3} \text{ m/s} \)

(ii) Speed in km/h:
To convert from m/s to km/h, multiply by \( \frac{18}{5} \) (or \( \frac{3600}{1000} \)):
\( \text{Speed in km/h} = \frac{2}{3} \times \frac{18}{5} = \frac{12}{5} = 2.4 \text{ km/h} \)
In simple words: The swimmer covers 400 metres in 10 minutes (which is 600 seconds). Divide the distance by the seconds to get the speed in m/s, and then change it to km/h.

Exam Tip: Don't forget that the trip is round-trip, so the distance is 400 metres, not 200 metres. Always check if a journey involves going and returning.

Question 10. A distance of 14.4 km is covered in 2 horus 40 minutes. Find the speed in ms-1. With this speed Sakshi goes to her school, 240 m away from her house and then returns back. How much time, in all, will Sakshi take?
Answer: First, let's find Sakshi's speed in m/s:
Given distance = 14.4 km
Time taken = 2 hours 40 minutes = \( 2 \frac{40}{60} \text{ hours} = 2\frac{2}{3} \text{ hours} = \frac{8}{3} \text{ hours} \)
Let's convert distance to metres and time to seconds:
\( \text{Distance in metres} = 14.4 \times 1000 = 14400 \text{ m} \)
\( \text{Time in seconds} = \frac{8}{3} \times 3600 = 9600 \text{ seconds} \)
Now, calculate the speed in m/s:
\( \text{Speed} = \frac{\text{14400}}{9600} = 1.5 \text{ m/s} \)

Next, we find the time taken for the round trip to school:
One-way distance = 240 m
Total distance covered (going and returning) = \( 240 \text{ m} + 240 \text{ m} = 480 \text{ m} \)
Using the speed of 1.5 m/s, let's find the time taken:
\( \text{Time taken} = \frac{\text{Distance}}{\text{Speed}} = \frac{480}{1.5} = 320 \text{ seconds} \)
Converting 320 seconds to minutes and seconds:
\( \frac{320}{60} \text{ minutes} = 5 \text{ minutes and } 20 \text{ seconds} \)
In simple words: Convert the first distance into metres and the time into seconds to find the speed, which is 1.5 m/s. Then, double the school distance to 480 m and divide by this speed to get the total time of 5 minutes and 20 seconds.

Exam Tip: Pay close attention to unit conversions. Converting km to metres and hours/minutes to seconds is essential when finding speed in m/s. Be careful with division to avoid writing 50 minutes instead of 5 minutes.