You could also avoid calculation and easily estimate your way to the correct answer to save time on this problem.

As Mitch demonstrated, 1 mile per 12 min --> 5 miles per hr for the first part of the trip.

If Ross rides at half the speed for the return trip, then the overall average speed will certain be less than 5mph. Eliminate C, D, and E.

Half the speed would be 2.5mph, and he's going twice the distance at this speed. Clearly much more of his trip was spent at 2.5mph than 5mph, so the average speed should be closer to 2.5 than 5. That eliminates B, leaving us only with A.

swerve wrote: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 a different path for onward and returns 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

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