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

Answer:

7 mph

Step-by-step 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 $\dfrac{22.5}{x-2}$ hours.

The time to go downstream $\dfrac{22.5}{x+2}$ hours.

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

$\dfrac{22.5}{x-2}-\dfrac{22.5}{x+2}=2\\ \\22.5\left(\dfrac{1}{x-2}-\dfrac{1}{x+2}\right)=2\\ \\22.5\cdot \dfrac{x+2-x+2}{(x-2)(x+2)}=2\\ \\\dfrac{22.5\cdot 4}{x^2-4}=2\\ \\x^2-4=22.5\cdot 2\\ \\x^2-4=45\\ \\x^2 =49\\ \\x=\pm 7$

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