Paul walks from home to work at a rate of 5 mph and bikes home from work along the same route at 12 mph. What is his average speed for the round trip?

Question

Manish Verma · Accepted Answer

Since we have an average rate question we can use the following formula:
average rate = total distance / total time
Since the distance is the same in both directions, we can use a smart number to represent the one-way distance. A good number to use would be one that is divisible by both 5 and 12, so we can let the distance each way = 60.
So, the time going to work is 60/5 = 12, and the time going home from work is 60/12 = 5.
Finally we can determine the average rate:
average rate = total distance / total time
average rate = (60 + 60)/(12 + 5)
average rate = 120/17