Question

Can someone walk me threw this problem?
(Intro to Technical Mathematics) I have to do to the unit analysis to make the the necessary conservation.

A marathon is a long distance running event that covers a distance of 26.2 miles. If the average runner can run 515 feet in one minute, how many hours will it take to complete the marathon.

Answer 1

\[s\left[\text {LT}^{-1}\right]=\frac {d\left[\text {L}\right]}{t\left[\text {T}\right]}\qquad\implies\qquad t\left[\text {T}\right]=\frac {d \left[\text {L}\right]}{s\left[\text {LT}^{-1}\right]}\]

Answer 2

\[{1[\text {hr}]}={60[\text{min}]}\qquad\implies\qquad\frac{[\text {hr}]}{60[\text{min}]}=1\]
\[{1[\text{mi}]}={5280[\text {ft}]}\qquad\implies\qquad \frac{5280[\text {ft}]}{[\text{mi}]}=1\]

Answer 3

\[t\left[\text {hr}\right]=\frac { 26.2\left[\text {mi}\right]}{515\left[\text {ft min}^{-1}\right]}\times1\times 1\]\[t\left[\text {hr}\right]=\frac { 26.2\left[\text {mi}\right]}{515\left[\text {ft min}^{-1}\right]}\times\frac{[\text {hr}]}{60[\text{min}]}\times \frac{5280[\text {ft}]}{[\text{mi}]}\]