Question

A boat traveled 280 miles each way downstream and back. The trip downstream took 10 hours. The trip back took 20 hours. Find the speed of the boat in still water and the speed of the current

Answer 1

Let x mi/h be the speed of the boat in still water and y mi/h be the speed of stream.

1) Downstream.

The speed of the boat travelling downstream is x+y mi/h. Then

`(x+y)\cdot 10=280.`

2) Upstream.

The speed of the boat travelling upstream is x-y mi/h. Then

`(x-y)\cdot 20=280.`

3) Solve the system of equations:

`\left\{\begin{array}{l}(x+y)\cdot 10=280\\ \\(x-y)\cdot 20=280\end{array}\right.\Rightarrow \left\{\begin{array}{l}x+y=28\\ \\x-y=14\end{array}\right..`

Add these two equations:

`x+y+x-y=28+14,\\ \\2x=42,\\ \\x=21\text{ mi/h}.`

Subtract these two equations:

`x+y-x+y=28-14,\\ \\2y=14,\\ \\y=7\text{ mi/h}.`

Answer: the speed of the boat in still water is 21 miles per hour and the speed of the stream is 7 miles per hour.