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# Two trains, each 100 meters long take 60 seconds to cross each other

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Math Expert
Joined: 02 Sep 2009
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Two trains, each 100 meters long take 60 seconds to cross each other  [#permalink]

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03 Jan 2020, 01:16
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Difficulty:

35% (medium)

Question Stats:

80% (02:17) correct 20% (02:06) wrong based on 15 sessions

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Two trains, each 100 meters long take 60 seconds to cross each other if traveling in the same direction and 10 seconds to cross each other when traveling in opposite direction. Find the speed of the faster train.

A. 30 kmph
B. 35 kmph
C. 42 kmph
D. 50 kmph
E. 84 kmph

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Re: Two trains, each 100 meters long take 60 seconds to cross each other  [#permalink]

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03 Jan 2020, 01:40
1
Approach:

- Assume the speed of trains be S1 and S2.

- Total Distance = length of both trains: 100+100 = 200 m
- Time taken T1 = 60 sec, T2 = 10 sec

- S1+S2 = 200/10 => 20 m/s ....1
- S1-S2 = 200/60 => 10/3 m/s ....2

- Add (1)&(2), We get S1 = 35/3 m/s and further S2 = 25/3 m/s

- speed of the faster train(in Kmph) 35/3*18/5 = 42Kmph

Option C
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Two trains, each 100 meters long take 60 seconds to cross each other  [#permalink]

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03 Jan 2020, 10:15
Bunuel wrote:
Two trains, each 100 meters long take 60 seconds to cross each other if traveling in the same direction and 10 seconds to cross each other when traveling in opposite direction. Find the speed of the faster train.

A. 30 kmph
B. 35 kmph
C. 42 kmph
D. 50 kmph
E. 84 kmph

Let the two speeds be v1 and v2, with v1 > v2.

Same direction: If we treat v2 as stationary, the speed of the faster train is effectively v1 - v2. The faster train needs to travel 200 meters to fully cross the slower train (since each train is 100 meters long). Then $$\frac{200 }{ {v1 - v2}} = 60$$ seconds.

Opposite direction: If we treat either stationary, the speed of the other train is effectively v1 + v2. Then $$\frac{200 }{ {v1 + v2}} = 10$$ seconds.

So we get $$v1 + v2 = 20$$ m/s and $$v1 - v2 = 10/3$$ m/s. We can add the equations to get $$2* v1 = 70/3$$ m/s and $$v1 = 35/3$$ m/s . Finally convert to kmph by multiplying $$\frac{{1 km} }{ {1000 m}}$$ and $$\frac{{3600 s} }{ {1 h}}$$,

$$\frac{35}{3} * \frac{3600 }{ 1000} = 35 * \frac{1200 }{ 1000} = 35 * \frac{6 }{ 5} = 42$$

Ans: C
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Re: Two trains, each 100 meters long take 60 seconds to cross each other  [#permalink]

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03 Jan 2020, 11:04
Two trains, each 100 meters long take 60 seconds to cross each other if traveling in the same direction and 10 seconds to cross each other when traveling in opposite direction. Find the speed of the faster train.

A. 30 kmph
B. 35 kmph
C. 42 kmph
D. 50 kmph
E. 84 kmph

Distance is same in both cases

200/relative speed = 60(In the same direction)

200/x - y = 60
x - y = 200/60
= 10/3---------(1)
200/x + y = 10
x + y = 20 ---------(2)

Considering (1) and (2) equations, 2 x = 20 +10/3
2 x = 60 + 10/3
x = 35/3(18/5)
= 42 KMPH(C)
Re: Two trains, each 100 meters long take 60 seconds to cross each other   [#permalink] 03 Jan 2020, 11:04
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