Dimensional Analysis Problem Help

Question

A runner runs 4875 feet in 6.85 minutes. What is the runners speed in miles per hour?

1 mile = 5280 feet

Answer 1

4875/5280 = 0.92233 = 92.233% of a mile

To find how long it takes to run a full mile, let X= minutes to run a mile. Then

X/5280 = 6.85/4875 The ratio of minutes to miles is the same

X = 6.85(5280)/4875 = 7.419 minutes

Now convert 1 mile per 7.419 minutes to one mile per hour. 60 minutes = 1 hour

divide 7.419 by 60 = 0.1237 hours to run a mile. invert hours per mile to miles per hour

Invert 0.1237

Divide 1 by 0.1237

1/0.1237 = 8,.084 mph

Or a faster way is:

4875/5280 = .92233 miles

If .92233 miles can be run in 6.85 minutes then divide by 60 to get

.92233 miles in 0.1142 hours

divide .92233 by 0.1142 = 8.08 mph