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Two trains, X and Y, started simultaneously from opposite en [#permalink]
23 Jun 2020, 04:58

Expert's post

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Question Stats:

66% (02:56) correct
33% (02:18) wrong based on 9 sessions

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]
23 Jun 2020, 05:21

1

This post received KUDOS

Expert's post

Carcass wrote:

Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5 (B) 40.0 (C) 60.0 (D) 62.5 (E) 77.5

Train X completed the 100-mile trip in 5 hours Speed = distance/time = 100/5 = 20 mph

Train Y completed the 100-mile trip in 3 hours Speed = distance/time = 100/3 ≈ 33 mph (This approximation is close enough. You'll see why shortly)

How many miles had Train X traveled when it met Train Y? Let's start with a word equation.

When the two trains meet, each train will have been traveling for the same amount of time So, we can write: Train X's travel time = Train Y's travel time

time = distance/speed We know each train's speed, but not the distance traveled (when they meet). So, let's assign some variables.

Let d = the distance train X travels So, 100-d = the distance train Y travels (since their COMBINED travel distance must add to 100 miles)

We can now turn our word equation into an algebraic equation. We get: d/20 = (100 - d)/33 Cross multiply to get: (33)(d) = (20)(100 - d) Expand: 33d = 2000 - 20d Add 20d to both sides: 53d = 2000 So, d = 2000/53

IMPORTANT: Before you start performing any long division, first notice that 2000/50 = 40 Since the denominator is greater than 50, we can conclude that 2000/53 is LESS THAN 40 Since only one answer choice is less than 40, the correct answer must be A

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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]
27 Jun 2020, 15:28

2

This post received KUDOS

Speed = distance / time

Train X speed is 100/5 = 20 miles per H Train Y speed is 100/3 = ~33 miles per H

Lets say that the Trains will meet each other after Time T. Therefore, Dist Traveled by X + Distance Traveled by Y = 100 miles 20T + 33T = 100 T = 100/53 = 1,88

it will take 1,88H for the train to meet. With train X speed of 20 miles per hour, distance = 20*1,88 = 37.7 =~37.5 (because of using 33 for speed of train Y instead of 100/3)

Answer A
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Re: Two trains, X and Y, started simultaneously from opposite en
[#permalink]
27 Jun 2020, 15:28