Round trip
Weekly Problem 42 - 2013
I walk to the bike shop, and then cycle back. What is my average speed for the combined journey?
I walk to the bike shop, and then cycle back. What is my average speed for the combined journey?
Age
11 to 14
Challenge level
Problem
I walk to the bike shop at 3 miles per hour, and I cycle home at 12 miles per hour. What is my average speed, in miles per hour, for the time that I am actually on the route?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Suppose the distance to and from the bike shop is $x$ miles.
Then the time taken on the journey there is $\frac{x}{3}$ hours, and the time taken on the journey back is $\frac{x}{12}$ hours.
So altogether a distance of $2x$miles is travelled in $\frac{x}{3} + \frac{x}{12} = \frac{5x}{12}$ hours.
So the average speed is $2x \div \frac{5x}{12} = 4.8$ miles per hour.