Question

A runner completed a 26.2-mile marathon in 210 minutes.

a. Estimate the unit rate, in miles per minute. Round your answer to the nearest hundredth of a mile.


b. Estimate the unit rate, in minutes per mile. Round your answer to the nearest tenth of a minute.

c. Another runner says, “I averaged 10-minute miles in the marathon.” Is this runner talking about the kind of rate described in part (a) or in part (b)? Explain your reasoning.

Answer 1

A)

This means in one minute, which is 1/210 of the total time, they would have ran 1/210 of the total distance.

So the runner would have ran 26.2/210 miles per minute, which is 0.12476 miles.

Rounding to the nearest hundredth of a mile,

They ran 0.12 miles per minute, so the unit rate is 0.12 miles per minute.

B)

You can work out the minutes per mile using the same concept.

For one mile, the runner would have ran 1/26.2 of the total time, so they ran 210/26.2 minutes per mile, or 8.015 minutes per mile.

Rounding to the nearest tenth, you'd round down to 8.0 minutes per mile.

So they ran 8.0 minutes per mile.

2) C)

For C, the other runner talks about the same rate as b), not a). This is because they are referring to the time they took to run one mile, so the other runner ran 10 minutes to cover one mile, or as they say, "10 minute miles", which is the rate in minutes per mile.

If they were referring to the rates in a), that would imply the other runner ran 10 miles per minute... which is very unlikely.