Question

The speed of the current in a stream is 2 mi/hr. It takes a canoeist 120 minutes longer to paddle 22.5 miles upstream than to paddle the same distance downstream. What is the canoeist's rate in still water?

Answer 1

7 mph

Explanation:

Let x mph be the canoeist's rate in still water.

The speed of the current in a stream is 2 mph, then

• the canoeist's rate upstream is x-2 mph;
• the canoeist's rate downstream is x+2 mph.

The distance covered is 22.5 miles.

The time to go upstream
`(22.5)/(x-2)` hours.

The time to go downstream
`(22.5)/(x+2)` hours.

It takes a canoeist 120 minutes (= 2 hours) longer to paddle 22.5 miles upstream than to paddle the same distance downstream, then

`(22.5)/(x-2)-(22.5)/(x+2)=2\\ \\22.5\left((1)/(x-2)-(1)/(x+2)\right)=2\\ \\22.5\cdot (x+2-x+2)/((x-2)(x+2))=2\\ \\(22.5\cdot 4)/(x^2-4)=2\\ \\x^2-4=22.5\cdot 2\\ \\x^2-4=45\\ \\x^2 =49\\ \\x=\pm 7`

The canoeist's rate cannot be negative, then his rate in still water is 7 mph.