Problem Solving

Gmat_mission wrote: ↑

Wed Feb 23, 2022 8:41 am

A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? (Assume that the driver did not make any stops during the 40-mile trip.)

(A) 65 mph
(B) 68 mph
(C) 70 mph
(D) 75 mph
(E) 80 mph

Answer: D

Source: Official Guide

Average speed = (total distance)/(total time)
We already know that the total distance travelled = 40 miles
And we know that we want the average speed to be 60 miles per hour
So, our equation becomes: 60 = 40/(total time)
We can rearrange this equation to get: total time = 40/60 = 2/3 hours

During the first part of the trip, the driver travels 20 miles at a speed of 50 mph
Time to complete first part = distance/rate = 20/50 = 2/5 hours

During the second part of the trip, the driver travels 20 miles at an unknown speed. So let's say that speed is x mph
Time to complete second part = distance/rate = 20/x = 20/x hours

At this point we have enough information to create the following equation: 2/5 + 20/x = 2/3
To eliminate the fractions we'll multiply both sides of the equation by 15x to get: 6x + 300 = 10x
Subtract 6x from both sides to get: to get: 300 = 4x
Solve: x = 300/4 = 75

Answer: D