Problem Solving

BTGmoderatorDC wrote: ↑

Sat Jul 09, 2022 7:32 pm

Every day in the morning Ross cycles for 2 hours. He always starts at a constant rate of 1 mile of distance in every 12 minutes. However, he takes different path for onward and return journey – the distance covered in the return journey is double of the distance covered in his onward journey. Also, his speed in the return journey becomes half of his original speed. What is his average speed in the whole journey?

A. 3 mph
B. 4 mph
C. 5 mph
D. 6 mph
E. 7 mph


OA A

Source: e-GMAT

If Ross cycles 1 mile every 12 minutes, then his rate is 5 miles per hour. Since he cycles 2 hours every morning, the times for the onward and return journeys are 1 hour each, and thus the distances for the onward and return journeys are 5 miles each.

However, since one morning he takes a different return path that is twice the onward path, his return path is 10 miles. Furthermore, since his return speed is half his original speed, his return speed is 2.5 miles per hour. Therefore, the time for the return journey is 10/2.5 = 4 hours. Since the distance and time for the onward journey remain 5 miles and 1 hour, respectively, then his average speed for the entire journey is:

(5 + 10)/(1 + 4) = 15/5 = 3 mph

Answer: A