Question

A boat crew rowed 105 kilometers downstream, with the current, in 5 hours. The return trip upstream, against the current, covered the same distance, and it took 21 hours. Find the crew is rowing rate in still water.rowing rate=_______ kilometers per hour

Answer 1

It's important to notice that downstream indicates that the river goes in the same direction that the boat crew, so we add; while upstream they have opposite directions so we subtract.

First, we find the ratio in each case.

$\begin{gathered} \text{down}=\frac{105\operatorname{km}}{5hr}=21\operatorname{km}/hr \\ up=\frac{105\operatorname{km}}{21hr}=5\operatorname{km}/hr \end{gathered}$

Then, we form the following system

$\begin{gathered} x+y=21 \\ x-y=5 \end{gathered}$

The first equation is with the current and the second one is against. Let's combine the equations and solve for x

$\begin{gathered} x+x+y-y=21+5 \\ 2x=26 \\ x=\frac{26}{2} \\ x=13 \end{gathered}$

Therefore, the rowing rate in still water is 13 kilometers per hour.