Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50%

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Jun 18, 2020 5:38 am

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Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

A. 20 miles per hour
B. 25 miles per hour
C. 30 miles per hour
D. 35 miles per hour
E. 40 miles per hour

Answer: C
Source: Manhattan prep

Source: Beat The GMAT — Problem Solving | Thu Jun 18, 2020 5:38 am

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Re: Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50%

by Brent@GMATPrepNow » Sun Jun 21, 2020 5:45 am

BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:38 am
Car X is 40 miles west of Car Y. Both cars are traveling east, and Car X is going 50% faster than Car Y. If both cars travel at a constant rate and it takes Car X 2 hours and 40 minutes to catch up to Car Y, how fast is Car Y going?

A. 20 miles per hour
B. 25 miles per hour
C. 30 miles per hour
D. 35 miles per hour
E. 40 miles per hour

Answer: C
Source: Manhattan prep

Let's let Car X's original position be the initial starting point.
So, when Car X is at the initial starting point, Car Y has already traveled 40 miles.

My word equation involves the conditions when Car X catches up to Car Y.
At that point, we can say:
Car X's TOTAL distance traveled = Car Y's TOTAL distance traveled

Car Y's total distance
Let V = Car Y's speed (our goal is to find the value of V)
From the time that Car X begins moving, Car Y drives for 2 2/3 hours (2 hours, 40 minutes).
So Car Y's total distance = (time)(speed) = (2 2/3)(V) + 40 miles

Car X's total distance
We know that Car X is going 50% faster than Car Y. If Car Y's rate is V, then Car X's rate must be 1.5V
We also know that Car X travels for 2 2/3 hours.
So Car X's total distance = (time)(speed) = (2 2/3)(1.5V) miles
Simplify: (2 2/3)(1.5V) = (8/3)(3/2) = 4V

We're now ready to write our algebraic equation.
Car X's total distance = Car Y's total distance
4V = (2 2/3)(V) + 40 miles
4/3V = 40
V = 40(3/4)
V = 30

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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