Ratio and Proportion Word Problems: Treadmill

Time $= \frac{ \mbox{Distance} } { \mbox{Speed} }$ .

Solution 1: Since he runs 6 miles per hour, it will take him $\frac { 13 } {6}$ hours, or equivalently $\frac {13 } { 6} \times 60 = 130$ minutes.

Solution 2: Since he runs 6 miles per hour, it will take him $\frac {60}{6} = 10$ minutes to run 1 mile. Hence, it will take him $10 \times 13 = 130$ minutes to run 13 miles.

Because Calvin can run on a treadmill at $6$ miles per hour, Calvin runs $60 \div 6 = 10$ miles per minute. To run $13$ miles, Calvin needs $10 * 13 = 130$ minutes.

$\dfrac{6 \text{ miles}}{60 \text{ minutes}} \implies \dfrac{1 \text{ mile}}{10 \text{ minutes}} \implies \dfrac{13 \text{ miles}}{\boxed{130} \text{ minutes}}$