Speed, Time and Distance
- Two trains of which one is 50 metres longer than the other are running in opposite directions and cross each other in 10 seconds. If they be running in the same direction then faster train would have passed the other train in 1 minute 30 seconds. The speed of faster train is 90 km per hr. Find the speed of other train.
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Let the length of trains be x m and (x + 50)m and the speed of other train be y m per sec.
The speed of the first train = 90 km per hr.= 90 × 5 = 25 m per sec. 18
Case : I Opposite direction,
Their relative speed = (y + 25)m per sec.
Distance covered = x + x + 50 = 2x + 50 metres∴ Time taken = 2x + 50 = 10 y + 25
⇒ 2x + 50 = 10y + 250 ...(i)
Case II. Direction is Same
Their relative speed = (25 – y) m per sec.
Distance covered = x + x + 50 = 2x + 50m∴ Time taken = 2x + 50 = 90 25 − y
⇒ 2x + 50 = 90 (25 – y) ...(ii)
From equations (i) and (ii)
10y + 250 = 2250 – 90y
⇒ 10y + 90y = 2250 – 250⇒ y = 2000 = 20 100
Putting y = 20 in equation (i), we have
2x + 50= 10 × 20 + 250 = 450
⇒ 2x = 450 – 50 = 400⇒ x = 400 = 200 2
∴ x + 50 = 200 + 50 = 250 metres.
Hence,
The length of the 1st train = 200 metres.
The length of the 2nd train = 250 metres.
The speed of the 2nd train = 20 m per sec.Correct Option: B
Let the length of trains be x m and (x + 50)m and the speed of other train be y m per sec.
The speed of the first train = 90 km per hr.= 90 × 5 = 25 m per sec. 18
Case : I Opposite direction,
Their relative speed = (y + 25)m per sec.
Distance covered = x + x + 50 = 2x + 50 metres∴ Time taken = 2x + 50 = 10 y + 25
⇒ 2x + 50 = 10y + 250 ...(i)
Case II. Direction is Same
Their relative speed = (25 – y) m per sec.
Distance covered = x + x + 50 = 2x + 50m∴ Time taken = 2x + 50 = 90 25 − y
⇒ 2x + 50 = 90 (25 – y) ...(ii)
From equations (i) and (ii)
10y + 250 = 2250 – 90y
⇒ 10y + 90y = 2250 – 250⇒ y = 2000 = 20 100
Putting y = 20 in equation (i), we have
2x + 50= 10 × 20 + 250 = 450
⇒ 2x = 450 – 50 = 400⇒ x = 400 = 200 2
∴ x + 50 = 200 + 50 = 250 metres.
Hence,
The length of the 1st train = 200 metres.
The length of the 2nd train = 250 metres.
The speed of the 2nd train = 20 m per sec.
- Two places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet each other in 8 hours. If they move in opposite directions towards each other, they meet in 1 hour 20 minutes. Determine the speed of the faster car.
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Case : I
When the cars are moving in the same direction.
Let A and B be two places and C be the place of meeting.
Let the speed of car starting from A be x kmph, and that of car starting from B be y kmph.
Relative speed = (x – y) kmph
According to the question.
(x – y) × 8 = 80
⇒ x – y = 10 ...(i)
Case : II
When the cars are moving in the opposite directions and they meet at point C.
Relative speed = (x + y) kmph
Time taken = 1 hour 20 minutes= 1 + 1 = 4 hours 3 3 ∴ (x + y) × 4 = 80 3 ⇒ x + y = 80 × 3 4
⇒ x + y = 60 ...(ii)
Adding equations (i) and (ii),
2x = 70
⇒ x = 35
From equation (ii),
x + y = 60
⇒ 35 + y = 60
⇒ y = 60 – 35 = 25
∴ Speed of the faster car = 35 kmphCorrect Option: C
Case : I
When the cars are moving in the same direction.
Let A and B be two places and C be the place of meeting.
Let the speed of car starting from A be x kmph, and that of car starting from B be y kmph.
Relative speed = (x – y) kmph
According to the question.
(x – y) × 8 = 80
⇒ x – y = 10 ...(i)
Case : II
When the cars are moving in the opposite directions and they meet at point C.
Relative speed = (x + y) kmph
Time taken = 1 hour 20 minutes= 1 + 1 = 4 hours 3 3 ∴ (x + y) × 4 = 80 3 ⇒ x + y = 80 × 3 4
⇒ x + y = 60 ...(ii)
Adding equations (i) and (ii),
2x = 70
⇒ x = 35
From equation (ii),
x + y = 60
⇒ 35 + y = 60
⇒ y = 60 – 35 = 25
∴ Speed of the faster car = 35 kmph
- In a one-kilometre race, A beats B by 15 seconds and B beats C by 15 seconds. If C is 100 metres away from the finishing mark, when B has reached it, find the speed of A.
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Let B take x seconds to run 1000 m.
∴ Time taken by C
= (x + 15) seconds∴ x = 900 = 9 x + 15 1000 10
⇒ 10x = 9x + 135
⇒ x = 135 seconds
Now in a one kilometre race, A beats B by 15 seconds.
It means A covers 1000 m in
135 – 15 = 120 seconds∴ Speed of A = 1000 = 25 m/sec 120 3
= 8.3 m/sec.Correct Option: D
Let B take x seconds to run 1000 m.
∴ Time taken by C
= (x + 15) seconds∴ x = 900 = 9 x + 15 1000 10
⇒ 10x = 9x + 135
⇒ x = 135 seconds
Now in a one kilometre race, A beats B by 15 seconds.
It means A covers 1000 m in
135 – 15 = 120 seconds∴ Speed of A = 1000 = 25 m/sec 120 3
= 8.3 m/sec.
- A train running at the speed of 72 km/hr passes a tunnel completely in 3 minutes. While inside the tunnel, it meets another
direction at the speed of 90km/hr and passes it completely intrain of 3 of its length coming from opposite 4 3 1 seconds. Find the length of the tunnel. 2
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Trains are running in opposite directions.
∴ Relative speed = 72 + 90
= 162 kmph= 162 × 5 = 45 m/sec 18
Let the length of the first train be = x metre.
∴ Length of the second train= 3 x meter. 4
Now,distance travelled in 3 1 seconds at 45 m/sec. 2 = 45 × 7 = 315 metre 2 2
This distance is equal to sum of the lengths of trains.∴ x + 3x = 315 4 2 ⇒ 4x + 3x = 315 4 2 ⇒ 7x = 315 4 2 ⇒ x = 315 × 4 = 90 2 7
Hence, the length of the first train = 90 metre.
Speed of first train = 72 kmph= 72 × 5 = 20 m/sec 18
Time taken by the first train to cross the tunnel
= 3 minutes = 180 seconds
∴ Distance covered by it in 180 seconds
= 180 × 20 = 3600 metre
∴ Length of (first train + tunnel) = 3600 metre
∴ Length of tunnel
= 3600 – 90 = 3510 metreCorrect Option: A
Trains are running in opposite directions.
∴ Relative speed = 72 + 90
= 162 kmph= 162 × 5 = 45 m/sec 18
Let the length of the first train be = x metre.
∴ Length of the second train= 3 x meter. 4
Now,distance travelled in 3 1 seconds at 45 m/sec. 2 = 45 × 7 = 315 metre 2 2
This distance is equal to sum of the lengths of trains.∴ x + 3x = 315 4 2 ⇒ 4x + 3x = 315 4 2 ⇒ 7x = 315 4 2 ⇒ x = 315 × 4 = 90 2 7
Hence, the length of the first train = 90 metre.
Speed of first train = 72 kmph= 72 × 5 = 20 m/sec 18
Time taken by the first train to cross the tunnel
= 3 minutes = 180 seconds
∴ Distance covered by it in 180 seconds
= 180 × 20 = 3600 metre
∴ Length of (first train + tunnel) = 3600 metre
∴ Length of tunnel
= 3600 – 90 = 3510 metre
- The average speed of a car is 75 km/h. The driver first decrease its average speed by 40% and then increase it by 50%. What is the new average speed now ?
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Required average speed = 75 x {(100 - 40)/100} x {(100 + 50)/100}
Correct Option: A
Required average speed = 75 x {(100 - 40)/100} x {(100 + 50)/100}
= 75 x 3/5 x 3/2
= 67.5 km/h
