Both car A and car B set out from their original locations

BTGmoderatorLU wrote:Source: Veritas Prep

Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?

A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00

The OA is C

Say the distance between Morse to Houston is d miles; thus Car A drove d miles, while Car B drove 2d miles, and took 2 hours more than Car A.

Time taken by Car A to cover d miles = d/65 hours;
Time taken by Car B to cover 2d miles = 2d/50 = d/25 hours;

=> d/25 = d/65 + 2

=> d = 65*5/4 hours

Time taken by Car A to cover d miles = d/65 hours = (65*5)/(65*4) = 1.25 hours

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorLU wrote:Source: Veritas Prep

Both car A and car B set out from their original locations at exactly the same time and on exactly the same route. Car A drives from Morse to Houston at an average speed of 65 miles per hour. Car B drives from Houston to Morse at 50 miles per hour, and then immediately returns to Houston at the same speed and on the same route. If car B arrives in Houston 2 hours after car A, how many hours did it take car A to make its trip?

A. 0.50
B. 1.00
C. 1.25
D. 1.33
E. 2.00

The OA is C

We can let x = the time, in hours, car A has driven; thus, x + 2 = the time car B has driven. Also car B travels twice the distance that car A travels. So we can create the distance equation:

50(x + 2) = 2(65)(x)

50x + 100 = 130x

100 = 80x

x = 1.25

Answer: C