Question

Nick swam at a rate of 3km/he and ran at a rate of 9km/hr for total distance traveled of 58.5km. If he completed the race in 8.5 hours, how long did he take to complete each part of the race?

Answer 1

Let s be the number of hours that Nick swam and r the number of hours that he ran, then we can set the following system of equations:

$\begin{gathered} s\cdot3+r\cdot9=58.5 \\ s+r=8.5 \end{gathered}$

Solving the second equation for s, and substituting in the first equation we get:

$\begin{gathered} (8.5-r)\cdot3+r\cdot9=58.5 \\ 25.5-3r+9r=58.5 \\ 6r=33 \\ r=5.5 \end{gathered}$

Substituting r=5.5 in the second equation, and solving for s we get:

$\begin{gathered} s+5.5=8.5 \\ s=3 \end{gathered}$

Therefore he swam for 3 hours and ran 5.5 hours.