GMAT Problem Solving - A Driver Completed the First 20 Miles of a 40-Mile Trip at an Average Speed of 50 Miles Per Hour

Question: 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

‘A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour’ is a GMAT Problem Solving topic. GMAT quantitative reasoning section analyses the candidates' ability to solve mathematical, and quantitative problems and interpret graphic data. The question in this section comes with five options. Candidates need to choose the one which is correct. This section of the GMAT Quant exam comprises 31 questions that need to be completed in a 62 minutes time frame. GMAT Problem Solving analyses candidates' logical and analytical reasoning skills. In this section, candidates indicate the best five answer choices.

Solution and Explanation 

There is only one approach to solving this problem.

Explanation:
Given:

• A driver completed the first 20 miles
• The trip is of 40-mile
• An average speed of 50 miles per hour.

Find out:

• 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?

The average speed = (total distance)/(total time
As per the problem statement, we already know that the total distance travelled = 40 miles
We also 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
Now, subtract 6x from both sides to get: to get:
300 = 4x
x = 300/4
x = 75
Correct Answer: D

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