A very fast runner can run a half-mile in 2 minutes. Express the average rate in terms of miles per minute

Question

A very fast runner can run a half-mile in 2 minutes. Express the average rate in terms of miles per minute, minutes per mile, and miles per hour

Answer 1

Rate = half-mile in 2 minutes 

 

So in 1 minute, the runner will run 1/2 of a half-mile = a quarter-mile = 0.25 miles

 

So the average rate is 0.25 miles per minute 

 

To find the rate in minutes per mile, you can either go back to the original rate = half-mile in 2 minutes and multiply by 2 to find rate = one mile in 4 minutes, or you can realize that minutes per mile is the inverse of miles per minute so you can just invert 1/4 miles per minute to get 4 minutes per mile. 

 

To find the rate in miles per hour, figure out how far the runner could run in 60 minutes, which is 30 half-miles, or 15 miles per hour