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# A train takes 15 seconds to cross a bridge at 50 mph, and at

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A train takes 15 seconds to cross a bridge at 50 mph, and at [#permalink]  30 Apr 2019, 01:26
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50% (01:43) correct 50% (06:22) wrong based on 30 sessions
A train takes 15 seconds to cross a bridge at 50 mph, and at the same speed takes 10 seconds to cross the same bridge when the train's length is halved.

 Quantity A Quantity B Length of the bridge Original length of the train

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: A train takes 15 seconds to cross a bridge at 50 mph, and at [#permalink]  02 May 2019, 11:08
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Re: A train takes 15 seconds to cross a bridge at 50 mph, and at [#permalink]  03 May 2019, 01:42
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Expert's post
Recall the key formula

Distance = speed * time

Now, we do have actually two distances.

Let the bridge being B and the train is L

The common factor here is the speed = 50

1) $$\frac{B+L}{15} = 50$$

$$\frac{B+\frac{L}{2}}{10} = 50$$

Equate the two $$\frac{B+L}{15} = \frac{B+\frac{L}{2}}{10}$$

$$2(B + L) = 3(B + \frac{L}{2})$$

$$2B + 2L = 3B + \frac{3L}{2}$$

$$\frac{L}{2} = B$$

$$L = 2B$$

The length of the train is twice the length of the bridge.

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Re: A train takes 15 seconds to cross a bridge at 50 mph, and at [#permalink]  01 Jun 2019, 03:26
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Carcass wrote:
A train takes 15 seconds to cross a bridge at 50 mph, and at the same speed takes 10 seconds to cross the same bridge when the train's length is halved.

 Quantity A Quantity B Length of the bridge Original length of the train

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

------- APPROXIMATION STRATEGY------------
A train crosses a bridge when it's tail leaves the end of bridge i.e. it covers the distance equal to (Train length + Bridge length)

This Train takes 5 seconds less to cross the bridge if its length is halved.

That means these 5 seconds were taken to cross this length which is cut off now (given as half of train's length).

So, 5 seconds for covering half the length of train ------> meaning train covers 1.5 times its length in 15 seconds

So, bridge's length must be half of train's length

Re: A train takes 15 seconds to cross a bridge at 50 mph, and at   [#permalink] 01 Jun 2019, 03:26
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