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Two trains, X and Y, started simultaneously from opposite en

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

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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink] New post 23 Jun 2020, 04:58
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Re: Two trains, X and Y, started simultaneously from opposite en [#permalink] New post 23 Jun 2020, 05:21
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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] New post 27 Jun 2020, 15:28
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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] New post 01 Oct 2020, 05:49
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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


Here's another approach....

speed = distance/time
So, Train X's speed = 100/5 = 20 miles per hour
And Train Y's speed = 100/3 ≈ 33 miles per hour

So the shrink rate = 20 + 33 = 53 miles per hour.

At the beginning, the two trains are 100 miles apart.
time = distance/speed
So the time it takes for the trains to meet (i.e., the time it takes for the distance between the two trains to shrink from 100 miles to 0 miles) = 100/53 = a little bit less than 2 hours

How many miles had Train X traveled when it met Train Y?
Distance = (speed)(time)
So Train X's distance traveled = (20)(a little bit less than 2 hours) = a little bit less than 40 miles

Answer: A

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Re: Two trains, X and Y, started simultaneously from opposite en   [#permalink] 01 Oct 2020, 05:49
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