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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

1. They would have met in 100/(100/5+100/3) hrs =15/8 hrs 2. In that time X would have traveled, Time *speed =15/8 *20=37.5
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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]

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30 Jun 2017, 19:47

Another one that we can solve without putting pen to paper. We should always take our time when approaching questions to glance at the answers and use our intuition to solve quickly. This test is as much about being strategic as it is about being intelligent.

Here's the approach: Train Y travels at a speed of 100/3 which is about 33.33 miles per hour. In contrast, Train X travels at 100/5 = 20 miles per hour. Hence, after 2 hours, Train Y will have traveled 66.66 miles, and Train X will have traveled 40 miles, which means they would have passed each other at this point.

Therefore, we know Train X must have traveled less than 40 miles when it met with Train Y. Only Answer A is less than 40 miles.

We should always be on the lookout for "smart" approaches... Think like the test makers.

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