Selina Solutions Concise Mathematics Class 6 Chapter 17 Idea of Speed, Distance and Time Exercise 17(B) explains all the basic terms in an understandable language, which are important from the exam perspective. The solutions PDF contain multiple tricks to solve the difficult problems effortlessly. In-depth practice of these solutions helps students boost exam preparation, along with scoring more marks in the annual examination. Those who aspire to become experts in Mathematics, are suggested to follow Selina Solutions Concise Mathematics Class 6 Chapter 17 Idea of Speed, Distance and Time Exercise 17(B) PDF, from the below mentioned links.
Selina Solutions Concise Mathematics Class 6 Chapter 17: Idea of Speed, Distance and Time Exercise 17(B) Download PDF
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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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