BTGModeratorVI wrote: ↑

Sat Mar 21, 2020 9:52 am

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

Answer: A
Source: Official Guide

One approach...

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

Cheers,
Brent

BTGModeratorVI wrote: ↑

Sat Mar 21, 2020 9:52 am

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

Answer: A
Source: Official Guide

The combined distance traveled of the two trains was 100 miles. Each train traveled for t hours. We can create the distance equation:

100/5 * t + 100/3 * t = 100

Multiplying by 15, we have:

300t + 500t = 1500

800t = 1500

t = 15/8

Thus, train X traveled 15/8 x 100/5 = 15/8 x 20 = 37.5 miles by the time it reached Y.

Answer: A