Speed, Time and Distance
- A carriage driving in a fog passed a man who was walking at the rate of 6 km per hr. in the same direction. He could see the carriage for 4 minutes and it was visible to him up to a distance of 200 metres. Find the speed of the carriage.
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The distance covered by man in 4 minutes
= 6 × 1000 × 4 = 400 metres 60
The distance covered by carriage in 4 minutes
= 200 + 400 = 600 metres∴ 600 × 60 km per hr. 4 1000
= 9 km per hr.Correct Option: D
The distance covered by man in 4 minutes
= 6 × 1000 × 4 = 400 metres 60
The distance covered by carriage in 4 minutes
= 200 + 400 = 600 metres∴ 600 × 60 km per hr. 4 1000
= 9 km per hr.
- Two bullets were fired at a place at an interval of 12 minutes. A person approaching the firing point in his car hears the two sounds at an interval of 11 minutes 40 seconds. The speed of sound is 330 metres per second. What is the approximate speed of the car?
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If the car were not moving, the person would have heard the two sounds at an interval of 12 minutes. Therefore, the distance travelled by car in 11 minutes 40 seconds is equal to the distance that could have been covered by sound in 12 min – 11 min. 40 seconds = 20 seconds.
Distance covered by sound in 20 seconds
= 330 × 20 = 6600 m
In 11 min 40 seconds
or 700 seconds the car travels 6600 m.
In 1 second the car will travel6600 metre = 66 metre 700 7 ∴ 66 metre per second 7 = 66 × 18 km per hr. 7 5 = 1188 km per hr. 35 = 33 33 km per hr. ≈ 34 kmph 35 Correct Option: A
If the car were not moving, the person would have heard the two sounds at an interval of 12 minutes. Therefore, the distance travelled by car in 11 minutes 40 seconds is equal to the distance that could have been covered by sound in 12 min – 11 min. 40 seconds = 20 seconds.
Distance covered by sound in 20 seconds
= 330 × 20 = 6600 m
In 11 min 40 seconds
or 700 seconds the car travels 6600 m.
In 1 second the car will travel6600 metre = 66 metre 700 7 ∴ 66 metre per second 7 = 66 × 18 km per hr. 7 5 = 1188 km per hr. 35 = 33 33 km per hr. ≈ 34 kmph 35
- A and B start simultaneously at 5 km per hr. and 4 km per hr. from P and Q, 180 kms apart, towards Q and P respectively. They cross each other at M and after reaching Q and P turn back immediately and meet again at N. Find the distance MN.
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When A and B cross each other at M for the first time, they have together covered the whole distance PQ = 180 km.
When they meet again at N, they have together covered total distance equal to 3 times of PQ = 3 × 180 = 540 km.PM = 5 × 180 = 100 km 5 + 4
[Distance covered by each will be in the ratio of their speeds)QP + PN = 4 × 540 = 240 km 5 + 4
or PN = 240 – QP = 240 – 180 = 60 km.
Then, MN = PM – PN
= 100 – 60 = 40 km.Correct Option: B
When A and B cross each other at M for the first time, they have together covered the whole distance PQ = 180 km.
When they meet again at N, they have together covered total distance equal to 3 times of PQ = 3 × 180 = 540 km.PM = 5 × 180 = 100 km 5 + 4
[Distance covered by each will be in the ratio of their speeds)QP + PN = 4 × 540 = 240 km 5 + 4
or PN = 240 – QP = 240 – 180 = 60 km.
Then, MN = PM – PN
= 100 – 60 = 40 km.
- A car driving in the morning fog passes a man walking at 4 km per hr. in the same direction. The man can see the car for 3 minutes and visibility is upto a distance of 130 metres. Find the speed of the car.
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Distance covered by man in 3 minutes
= 
4 × 1000 
m × 3 minutes 60 minutes
=200 metres
Total distance covered by the car in 3 min.
= (200 + 130) m = 330 metres∴ Speed of the car = 330 m per min. 3
= 110 m per minutes= 110 1000 1 60 = 33 km per hr. 5
or 6.6 kmphCorrect Option: B
Distance covered by man in 3 minutes
= 4 × 1000 m × 3 minutes 60 minutes
=200 metres
Total distance covered by the car in 3 min.
= (200 + 130) m = 330 metres∴ Speed of the car = 330 m per min. 3
= 110 m per minutes= 110 1000 1 60 = 33 km per hr. 5
or 6.6 kmph
- Ram starts his journey from Bombay to Pune and simultaneously Mohan starts from Pune to Bombay. After crossing each other they finish their remaining
What is Mohan’s speed if Ram’s speed is 20 km per hr. ?journey in 6 1 and 4 hours respectively. 4
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Suppose that Ram and Mohan meet at A. Let Ram’s speed be x km per hr. and Mohan’s speed be y km per hr.Then AP = 25 x km x
and AB = 4y km.
Now, time taken by Ram in going fromB to A = 4y x
and the time taken by Mohan in going fromP to A = 25x . 4y
Obviously time taken is equal∴ 4y = 25x x 4y
⇒ 16y2 = 25x2⇒ y2 = 25 x2 16 ⇒ y = 5 x 4 ⇒ y = 5 x 4
Here, x = 20 km per hr.
∴ y = Mohan’s speed= 5 × 20 = 25 km per hr. 4 Correct Option: C
Suppose that Ram and Mohan meet at A. Let Ram’s speed be x km per hr. and Mohan’s speed be y km per hr.Then AP = 25 x km x
and AB = 4y km.
Now, time taken by Ram in going fromB to A = 4y x
and the time taken by Mohan in going fromP to A = 25x . 4y
Obviously time taken is equal∴ 4y = 25x x 4y
⇒ 16y2 = 25x2⇒ y2 = 25 x2 16 ⇒ y = 5 x 4 ⇒ y = 5 x 4
Here, x = 20 km per hr.
∴ y = Mohan’s speed= 5 × 20 = 25 km per hr. 4
