Selina Solutions Concise Mathematics Class 6 Chapter 17 Idea of Speed, Distance and Time contains accurate answers pertaining to speed, distance and time in the given exercise problems. The main intention of providing solutions is to increase analytical and problem solving proficiency among students. Students who aim to obtain expertise in Mathematics are suggested to practice textbook questions, using solutions PDF. For a stronghold on the topics, students can refer to Selina Solutions Concise Mathematics Class 6 Chapter 17 Idea of Speed, Distance and Time PDF, from the links offered below.
Chapter 17 discusses important problems relying on speed, distance and time. Students obtain the technique of solving complex problems with ease, using solutions PDF, designed by experts at BYJU’S.
Selina Solutions Concise Mathematics Class 6 Chapter 17: Idea of Speed, Distance and Time Download PDF
Exercises of Selina Solutions Concise Mathematics Class 6 Chapter 17: Idea of Speed, Distance and Time
Access Selina Solutions Concise Mathematics Class 6 Chapter 17: Idea of Speed, Distance and Time
Exercise 17(A)
1. A train covers 51 km in 3 hours. Calculate its speed. How far does the train go in 30 minutes?
Solution:
Given
A train covers 51 km in 3 hours
So, distance = 51 km
Time = 3 hours
Hence,
Speed = 51 km/ 3 hours
We get,
= 17 km/h
Now for 30 minutes
Speed = 17 km/h
Time = 0.5 hours
Hence,
Distance = 17 × 0.5
We get,
= 8.5 km
Therefore, train covered 8.5 km in 30 minutes
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.
Solution:
Given
A motorist travelled the distance 65 km in 2 hours and 10 minutes
So, distance = 65 km
Time = 2 hours 10 minutes
Hence,
Speed = 65 km / (2 hours + 10 minutes)
We know that,
1 km = 1000 m
1 hour = 60 min
= 65 (1000 m) / [2 (60 min) + 10 min]
= 65000 m/130 min
We get,
= 500 m/min
Therefore, the speed of a motorist in meter per minute is 500 m/min
3. A train travels 700 metres in 35 seconds. What is its speed in km/h?
Solution:
Given
A train travels 700 metres in 35 seconds
So, distance = 700 m
Time = 35 sec
Hence,
Speed = 700 m / 35 sec
1000 m = 1 km
1 m = 0.001 km
700 m = 0.001 × 700
= 0.7 km
3600 seconds = 1 hour
1 sec = 1 / 3600 hour
35 sec = 35 / 3600
Now,
Speed = Distance / Time
= [0.7 / (35/ 3600)]
We get,
= (0.7 × 3600) / 35
= 2520 / 35
= 72 km/h
Therefore, the speed of train is 72 km/h
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?
Solution:
Given
A racing car covered 600 km in 3 hours and 20 minutes
So, distance = 600 km
Time = 3 hours 20 minutes
Hence,
Speed = 600 km / (3 hours + 20 minutes)
= 600 (1000m) / [3(60 min) + 20 min]
We get,
= 600000m / 200 min
= 600000m / 200 (60 sec)
We get,
= 600000 / 12000 sec
= 50 m / sec
Thus, speed in meter per second is 50 m / sec
Now, the distance covered by car in 50 sec is calculated as below
Speed = 50 m / sec
Time = 50 sec
Hence,
Distance = 50 × 50
= 2500 m
= 2.5 km
Therefore, the distance covered by car in 50 seconds is 2.5 km
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
Solution:
(i) his speed
Given
Rohit goes 350 km in 5 hours
So, distance = 350 km
Time = 5 hours
Hence,
Speed = 350 km / 5 hours
We get,
= 70 km/h
Hence, Rohit speed is 70 km/h
(ii) the distance covered by Rohit in 6.2 hours
Given
Rohit goes 350 km in 5 hours
So, distance = 350 km
Time = 5 hours
Hence,
Speed = 350 km / 5 hours
We get,
= 70 km/h
Now, the distance covered by Rohit in 6.2 hours is calculated as below
Speed = 70 km/h
Time = 6.2 hours
Hence,
Distance = 70 × 6.2
= 434 km
Therefore, Rohit covers 434 km in 6.2 hours
(iii) the time taken by him to cover 210 km
Given
Rohit goes 350 km in 5 hours
So, distance = 350 km
Time = 5 hours
Hence,
Speed = 350 km / 5 hours
We get,
= 70 km/h
Now, the time taken by Rohit to cover 210 km is calculated as below
Distance = 210 km
Speed = 70 km/h
Hence,
Time = 210 km / 70 km/h
= 3 hours
Therefore, the time taken by Rohit to cover 210 km is 3 hours
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
(i) the distance covered by him in 1 hour 20 min
Given
Speed of scooter is 45 km/h
Speed = 45 km/h
Time = 1 hours 20 minutes
Hence,
Distance = 45 × (1 + 20 / 60)
= 45 × (1 + 1 / 3)
We get,
= 45 × 4 / 3
= 15 × 4
= 60
Hence, the distance covered by a boy in 1 hour 20 minutes is 60 km
(ii) the time taken by him to cover 108 km
Given
Speed of scooter is 45 km/h
So, speed = 45 km/h
Distance = 108 km
Hence,
Time = 108 km / 45 km/h
We get,
= 12 / 5 h
=Â 
h
This is equal to,
= 2 hours (2 / 5) × 60 min
= 2 hours (2 × 12) min
= 2 hours 24 min
Hence, the time taken by a boy to cover 108 km distance is 2 hours 24 min
(iii) the time taken to cover 900 m
Given
Speed of scooter is 45 km/h
So, speed = 45 km/h
Distance = 900 m
Hence,
Time = 900 m / 45 km/h
= (900 / 1000) × 1 / 45
We get,
= (9 / 10) × (1 / 45)
= 1 / 50 h
= (1 / 50) × 60 min
= 6 / 5 min
This can be written as,
= 1 and 1 / 5 min
= 1 min (1 / 5 × 60) sec
We get,
= 1 min 12 sec
Hence, the time taken by a boy to cover 900 m is 1 min 12 sec
7. I travel a distance of 10 km and come back in 2 ½ hours. What is my speed?
Solution:
Given
10 km distance travelled twice in 2 ½ hours
So, distance = 10 km + 10 km
= 20 km
Time = 2 ½ hours
This can be written as,
Time = 5 / 2 hours
Hence,
Speed = [20 km / (5 / 2 hours)]
= (20 × 2) / 5
We get,
= 40 / 5
= 8 km/h
Hence, the speed of a person to cover a distance of 10 km twice is 8 km/h
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 ½ hour. What was his average speed during the whole journey?
Solution:
Given
A man walks a distance of 5 km in 2 hours
40 km distance is covered by bus in 2 hours
5 km distance is covered by autorickshaw in ½ hour
Hence,
Total distance covered by a man during whole journey is calculated as below
Total distance = 5 km + 40 km + 5 km
= 50 km
Total time taken by a man during whole journey
Total time = 2 + 2 + 1/2
= (4 + 4 + 1) / 2
We get,
= 9 / 2 hours
Hence,
Average speed = 50 km / (9 / 2) hours
= (50 × 2) / 9 km/h
= 100 / 9 km/h
=
km/h
Therefore, the average speed taken by a man during whole journey is 
 km/h
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?
Solution:
Given
Jagan covered 240 km distance by a car at 60 km/h
He travelled 80 km distance by train at 100 km/h
He travelled 200 km distance by a bus at 50 km/h
Hence,
Total distance travelled by Jagan = 240 km + 80 km + 200 km
= 520 km
Now, total time taken by Jagan during whole journey is shown below
Time taken by car = 240 km / 60 km/h
= 4 hours
Time taken by a train = 80 km / 100 km/h
= 4 / 5 hours
Time taken by bus = 200 km / 50 km/h
= 4 hours
So, total time taken = 4 + 4 / 5 + 4
= (20 + 4 + 20) / 5
We get,
= 44 / 5 hours
Hence,
Average speed = total distance / total time
= 520 km / (44 / 5) hours
= [(520 × 5) / 44] km/h
= (130 × 5) / 11 km/h
= 650 / 11 km/h
=Â 
km/h
Hence, the average speed during the whole journey is 
km/h
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?
Solution:
Given
Speed of sound in air = 330 m/sec
So, speed = 330 m/sec
Distance = 99 km
= 99 × 1000
We get,
= 99000 m
Hence,
Time = [(99000 m) / (330 m/sec)]
= 9900 / 33 sec
We get,
= 300 sec
= 5 min
Hence, the time taken by the sound to travel 99 km is 5 min
Exercise 17(B)
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?
Solution:
Given
A train 180 m long is running at a speed of 90 km/h
So, distance = 180 m
Speed = 90 km/h
Hence,
Time = Distance / Speed
= 180 m / 90 km/h
= 180 / (90 × 1000)
= 1 / 500 hours
We get,
= 1 / 500 × 60 × 60 sec
= 36 / 5 sec
We get,
= 7.2 sec
Hence, the train will take 7.2 sec to pass a railway signal
2. A train whose length is 150 m, passes a telegraph pole in 10 sec. Find the speed of the train in km/h.
Solution:
Given
A train whose length is 150 m, passes a telegraph pole in 10 sec
So, distance = 150 m
Time = 10 sec
Hence,
Speed = 150 m / 10 sec
= 15 m/sec
= (15 × 60 × 60) / 1000 km/h
= (15 × 6 × 6) / 10 km/h
= 3 × 3 × 6 km/h
We get,
= 54 km/h
Hence, the speed of train in kilometer per hour is 54 km/h
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?
Solution:
Given
A train 120 m long passes a railway platform 160 m long in 14 seconds
Distance = 120 m + 160 m
= 280 m
Time = 14 sec
Hence,
Speed = Distance / time
= 280 / 14
= 20 m/sec
Hence, the speed of train is 20 m/sec
Now, time taken by the train to pass 100 m platform is as follows
Distance = 120 m + 100 m
= 220 m
Speed = 20 m/sec
Time = 220 m / 20 m/sec
We get,
= 11 sec
Hence, the time taken by the train to pass 100 m platform is 11 sec
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?
Solution:
(a) (i)
Given
8 km is covered in 1 hour 20 minutes
Distance = 8 km
Time = 1 hour 20 minutes
= 1 + 20 / 60
= 1 + 1 / 3
We get,
= 4 / 3 hours
Hence,
Speed = 8 km / (4 / 3) hours
Speed = (8 × 3) / 4 km/h
Speed = 2 × 3 km/h
Speed = 6 km/h
Now, distance covered in 10 minutes is as follows
Speed = 6 km/h
Time = 10 min
= 10 / 60 hour
= 1 / 6 hour
Hence,
Distance = 6 × 1 / 6
We get,
= 1 km
Therefore, the distance covered by Mr. Amit in 10 min is 1 km
(ii) Given
8 km is covered in 1 hour 20 minutes
So,
Distance = 8 km
Time = 1 hour 20 minutes
= 1 + 20 / 60
= 1 + 1 / 3
We get,
= 4 / 3 hours
Hence,
Speed = 8 km / 4 / 3 hours
= (8 × 3) / 4 km/h
We get,
= 6 km/h
Now, the distance covered in 30 seconds is as follows
Speed = 6 km/h
Time = 30 sec
Hence,
Distance = 6 × [30 / (60 × 60)] km
On further calculation, we get
= 1 / (10 × 2) km
= 1 / 20 × 1000 m
= 1 / 2 × 100
= 50 m
Therefore, the distance covered by Mr. Amit in 30 seconds is 50 m
(b) (i)
Given
8 km is covered in 1 hour 20 minutes
So,
Distance = 8 km
Time = 1 hour 20 minutes
= 1 + 20 / 60
We get,
= 1 + 1 / 3
= 4 / 3 hours
Hence,
Speed = 8 km / 4 / 3 hours
= (8 × 3) / 4 km/h
= (2 × 3) km/h
= 6 km/h
Now, time taken by Mr. Amit to walk 2500 m is as follows
Speed = 6 km/h
Distance = 2500 m
= 2.5 km
Hence,
Time = 2.5 / 6 hour
= 25 / (6 × 10) hour
On further calculation, we get
= 5 / 12 hour
= 5 / 12 × 60 min
= 5 × 5 min
= 25 min
Therefore, the time taken by Mr. Amit to walk 2500 m is 25 minutes
(ii)
Given
8 km is covered in 1 hour 20 minutes
So,
Distance = 8 km
Time = 1 hour 20 minutes
= 1 + 20 / 60
= 1 + 1 / 3
We get,
= 4 / 3 hours
Hence,
Speed = 8 km / 4 / 3 hours
= (8 × 3) / 4 km/h
= (2 × 3) km/h
= 6 km/h
Now, time taken by Mr. Amit to walk 6.5 km is as follows
Speed = 6 km/h
Distance = 6.5 km
Hence,
Time = 6.5 / 6 hour
= 65 / 60 hour
= 1 hour 5 minutes
Therefore, the time taken by Mr. Amit to walk 6.5 km is 1 hour 5 min
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?
Solution:
Given
First speed = 45 km/h
Second speed = 12.25 m/sec
= [(1225 × 60 × 60) / (100 × 1000)] km/h
= (1225 × 6 × 6) / 1000 km/h
On further calculation, we get
= (49 × 6 × 6) / 40 km/h
= (49 × 3 × 3) / 10 km/h
We get,
= 441 / 10 km/h
= 44.1 km/h
Hence, it is clear that the first speed 45 km/h is greater than the second speed 12.25 m/sec
Now, the distance travelled in 2 seconds at 45 km/h is shown below
Speed = 45 km/h
= (45 × 1000) / (60 × 60) m/sec
We get,
= 450 / 36 m/sec
Time = 2 sec
Hence,
Distance = 450 / 36 m/sec × 2 sec
= 450 / 18 m
= 25 m
Now, the distance travelled in 2 seconds at 12.25 m/sec is shown below
Speed = 12.25 m/sec
Time = 2 sec
Hence,
Distance = 12.25 m/sec × 2 sec
= 24.50 m
Therefore, the distance travelled by each in 2 seconds is 25 m and 24.50 m
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.
Solution:
(i) Same direction
Given
Speed of A = 15 km/h
Speed of B = 12 km/h
Time = 6 hours
Hence,
Distance covered by A = 15 × 6
= 90 km
Distance covered by B = 12 × 6
= 72 km
Now, the distance between A and B after 6 hours if both move in same direction is calculated as follows
Distance covered by A – Distance covered by B = 90 km – 72 km
= 18 km
Hence, the distance between A and B after 6 hours if both move in same direction is 18 km
(ii) the opposite direction
Given
Speed of A = 15 km/h
Speed of B = 12 km/h
Time = 6 hours
Hence,
Distance covered by A = 15 × 6
= 90 km
Distance covered by B = 12 × 6
= 72 km
Now, the distance between A and B after 6 hours if both move in the opposite directions can be calculated as shown below
Distance covered by A + Distance covered by B = 90 km + 72 km
= 162 km
Hence, the distance between A and B after 6 hours if both move in the opposite directions is 162 km
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?
Solution:
Given
Speed of A = 6 km/h
Speed of B = 2 m/sec
Time = 5 hours
Hence,
Distance covered by A = 6 km/h × 5 hours
We get,
= 30 km
Distance covered by B = 2 m/sec × 5 hours
= 2 × 5 × 60 × 60
We get,
= 36000 m
= 36 km
Hence, it is clear that B will be ahead of A
Now, the distance between B and A after 5 hours if both moving in the same direction is calculated as below
Distance covered by B – Distance covered by A = 36 km – 30 km
= 6 km
Hence, B will be ahead of 6 km from A
8. Mohit covers a certain distance in 6 hours 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
Solution:
(i)
Given
Mohit covers a distance at a speed of 40 km/h in 6 hours by his scooter
So,
Speed of scooter = 40 km/h
Time taken by scooter = 6 hours
Hence,
Distance = 40 × 6
We get,
= 240 km
Now, the time taken by Manjoor to cover 240 km by his car at the speed of 60 km/h is calculated as below
Time = 240 / 60
We get,
= 4 hours
Hence, the time taken by Manjoor to cover 240 km by his car at the speed of 60 km/h is 4 hours
(ii)
Given
Mohit covers a distance at a speed of 40 km/h in 6 hours by his scooter
So,
Speed of scooter = 40 km/h
Time taken by scooter = 6 hours
Hence,
Distance = 40 × 6
= 240 km
Now, the speed of Joseph to cover 240 km in 8 hours can be calculated as below
Speed = 240 / 8
= 30 km/h
Hence, the speed of Joseph to cover 240 km in 8 hours is 30 km/h
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
Solution:
(i) m/sec
Given
A boy swims 200 m in still water and then returns back to the starting point in total 10 minutes
So,
Distance = 200 m + 200 m
= 400 m
Time = 10 minutes
Hence,
Speed = 400 /10
We get,
= 40 m/min
Converting into seconds, we get
= 40 / 60 m/sec
= 2 / 3 m/sec
Therefore, the speed of the boy swim in meter per second is 2 / 3 m/sec
(ii) km/h
Given
A boy swims 200 m in still water and then returns back to the starting point in total 10 minutes
So,
Distance = 200 m + 200 m
= 400 m
Time = 10 minutes
Hence,
Speed = 400 / 10
= 40 m/min
Now, converting into km/h, we get
= (40 × 60) / 1000 km/h
We get,
= 24 / 10 km/h
= 2.4 km/h
Therefore, the speed of the boy swim in kilometer per hour is 2.4 km/h
10. A distance of 14.4 km is covered in 2 hours 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?
Solution:
Given
A distance of 14.4 km is covered in 2 hours 40 minutes
So,
Distance = 14.4 km
Converting into metre, we get
= 14.4 × 1000 m
= 14400 m
Time = 2 hours 40 minutes
Converting into seconds, we get
= 160 minutes
= 160 × 60 seconds
We get,
= 9600 seconds
Hence,
Speed = (14400 / 9600) m/sec
= 144 / 96 m/sec
We get,
= 3 / 2 m/sec
= 1.5 m/sec
Hence, the speed in meter per second is 1.5 m/sec
Now, time taken by Sakshi to cover the distance to go to her school, 240 m away from her house and then return back is calculated as below
Distance = 240 m + 240 m
= 480 m
Speed = 1.5 m/sec
Hence,
Time = 480 / 1.5 sec
= 4800 / 15 sec
We get,
= 320 sec
= 5 min 20 sec
Hence, Sakshi will take 5 minutes 20 seconds to go to her school and then return back
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