Question

Sue walked from her home to her school at a constant rate of 2 miles per hour, picked up her bicycle and rode back at a constant rate of 10 miles per hour. If the round trip took 1.5 hours, how far is the school from Sue's home?

Answer 1

15 miles

Explanation:

the 2 mph is a red herring. If there is a rate of 10 mph, and the trip took 1.5 hours, the 1 hour=10 miles, and the .5=5 miles, add em up and its 15 miles

Answer 2

Answer: the school is 2.5 miles from Sue's home.

Explanation:

Let x represent the distance of the school from Sue's home.

Time = distance/speed

Sue walked from her home to her school at a constant rate of 2 miles per hour. It means that the time it took her to walk to the school is

x/2

She picked up her bicycle and rode back at a constant rate of 10 miles per hour. The distance covered is the same and the time spent in riding back home is

x/10

If the round trip took 1.5 hours, it means that

x/2 + x/10 = 1.5

Multiplying through by 10, it becomes

5x + x = 15

6x = 15

x = 15/6

x = 2.5 miles