Speed, Time and Distance
- A train travelling at the rate of 60 km per hr, while inside a tunnel, meets another train of half its length travelling at 90 km per hr.
Find the length of the tunnel if the first train passes completelyand passes completely in 4 1 seconds. 2 through it in 4 minutes 37 1 seconds. 2
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Trains are running in opposite direction.
∴ Relative speed of the two trains
= 90 + 60 = 150 km per hr.Distance travelled in 4 1 seconds 2
with speed of 150 km per hr.= 150 × 5 m per sec. 18 = 150 × 5 × 9 18 2 = 375 metres 2
Let the length of the first train be x metres.Then the length of the second train be x metres 2 ∴ x + x = 375 2 2 ⇒ 3x = 375 2 2
⇒ 3x = 375
⇒ x = 125 metres
Hence, the length of the first
train = 125 metres
Speed of the first train = 60 km per hr.= 60 × 5 m per sec. 18 = 50 m per sec. 3
Time taken by the first train to cross the tunnel = 4 minutesand 37 1 sec. 2 = 240 + 75 sec. = 480 + 75 2 2 = 555 sec. 2 Speed of first train = 50 m per sec. 3 ∴ Distance covered by it in 555 sec. 2 = 50 × 555 = 4625 metres 3 2
Hence, length of tunnel
= 4625 – 125 = 4500 metres
= 4.5 kmCorrect Option: C
Trains are running in opposite direction.
∴ Relative speed of the two trains
= 90 + 60 = 150 km per hr.Distance travelled in 4 1 seconds 2
with speed of 150 km per hr.= 150 × 5 m per sec. 18 = 150 × 5 × 9 18 2 = 375 metres 2
Let the length of the first train be x metres.Then the length of the second train be x metres 2 ∴ x + x = 375 2 2 ⇒ 3x = 375 2 2
⇒ 3x = 375
⇒ x = 125 metres
Hence, the length of the first
train = 125 metres
Speed of the first train = 60 km per hr.= 60 × 5 m per sec. 18 = 50 m per sec. 3
Time taken by the first train to cross the tunnel = 4 minutesand 37 1 sec. 2 = 240 + 75 sec. = 480 + 75 2 2 = 555 sec. 2 Speed of first train = 50 m per sec. 3 ∴ Distance covered by it in 555 sec. 2 = 50 × 555 = 4625 metres 3 2
Hence, length of tunnel
= 4625 – 125 = 4500 metres
= 4.5 km
- A train overtakes two person walking at 2 km per hr. and 4 km per hr. respectively and
passes completely them in 9 sec. and 10 sec. respectively. What is the length of the train?
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Let the length of the train be x km and its speed y km per hr.
Case I : When it passes the man walking at 2 km per hr. in the same direction
Relative speed of train = (y – 2) km per hr.∴ x = 9 seconds y − 2 = 9 = 1 hour ...(i) 3600 400
Case II : When the train crosses the man walking at 4 km per hr. in the same direction.
Relative speed of train= (y – 4) km per hr.∴ x = 10 sec. y − 4 ⇒ x = 10 hrs. y − 4 3600 ⇒ x = 1 hrs. ...(ii) y − 4 360
On dividing equation (i) by (ii),
we havey − 4 = 1/400 = 360 = 9 y − 2 1/360 400 10
⇒ 10y – 40 = 9y – 18
⇒ 10y – 9y = 40 – 18
⇒ y = 22 km per hr.
∴ From equaton (i), we have⇒ x = 1 22 − 2 400 ⇒ x = 1 km 20 = 1000 = 50 metres. 20 Correct Option: D
Let the length of the train be x km and its speed y km per hr.
Case I : When it passes the man walking at 2 km per hr. in the same direction
Relative speed of train = (y – 2) km per hr.∴ x = 9 seconds y − 2 = 9 = 1 hour ...(i) 3600 400
Case II : When the train crosses the man walking at 4 km per hr. in the same direction.
Relative speed of train= (y – 4) km per hr.∴ x = 10 sec. y − 4 ⇒ x = 10 hrs. y − 4 3600 ⇒ x = 1 hrs. ...(ii) y − 4 360
On dividing equation (i) by (ii),
we havey − 4 = 1/400 = 360 = 9 y − 2 1/360 400 10
⇒ 10y – 40 = 9y – 18
⇒ 10y – 9y = 40 – 18
⇒ y = 22 km per hr.
∴ From equaton (i), we have⇒ x = 1 22 − 2 400 ⇒ x = 1 km 20 = 1000 = 50 metres. 20
- A train takes 18 seconds to pass completely through a station 162 metres long and 15 seconds to pass completely through another station 120 metres long. Find the speed of train in km per hr.
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Let the length of the train be x metres
Then, in 18 sec. the train travels (x + 162) metres ...(i)
and in 15 sec. the train travels (x + 120) metres
∴ In (18 – 15) = 3 sec. the train travels (x + 162)
– (x + 120) = 42m.∴ In 1 sec the train travels = 42 = 14 metres. ...(ii) 3
∴ In 18 sec. the train travels = 14 × 18 = 252 metres ...(iii)
From equations (i) and (iii)
∴ x + 162 = 252
⇒ x = 252 – 162 = 90
∴ Length of the train = 90 metres
Also, from equation (ii) we see
that in 1hr. the train travels
= 14 × 60 × 60 metres= 14 × 60 × 60 km = 50.4 km 1000
∴ The speed of the train
= 50.4 km per hr.Correct Option: A
Let the length of the train be x metres
Then, in 18 sec. the train travels (x + 162) metres ...(i)
and in 15 sec. the train travels (x + 120) metres
∴ In (18 – 15) = 3 sec. the train travels (x + 162)
– (x + 120) = 42m.∴ In 1 sec the train travels = 42 = 14 metres. ...(ii) 3
∴ In 18 sec. the train travels = 14 × 18 = 252 metres ...(iii)
From equations (i) and (iii)
∴ x + 162 = 252
⇒ x = 252 – 162 = 90
∴ Length of the train = 90 metres
Also, from equation (ii) we see
that in 1hr. the train travels
= 14 × 60 × 60 metres= 14 × 60 × 60 km = 50.4 km 1000
∴ The speed of the train
= 50.4 km per hr.
- A man perform 2/15 of the total journey by rail, 9/20 by tonga and the remaining 10 km on foot. This total journey is ?
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Let the total journey be x km. then,
2x/15 + 9x/20 + 10 = xCorrect Option: D
Let the total journey be x km. then,
2x/15 + 9x/20 + 10 = x
⇒ 8x + 27x + 600 = 60x
⇒ x = 24
∴ Total journey = 24 km.
- A speed of 30.6 km/hr. is the same as ?
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Speed in m/sec = speed in km/hr x (5 / 18 )
Speed in m/sec = ( 30.6 x 18 /5 ) m/secCorrect Option: B
Speed in m/sec = speed in km/hr x (5 / 18 )
Speed in m/sec = ( 30.6 x 18 /5 ) m/sec
= 8.5 m/sec
