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 distance covered is 22.5 miles.
The time to go upstream [tex]\dfrac{22.5}{x-2}[/tex] hours.
The time to go downstream [tex]\dfrac{22.5}{x+2}[/tex] hours.
It takes a canoeist 120 minutes (= 2 hours) longer to paddle 22.5 miles upstream than to paddle the same distance downstream, then
[tex]\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[/tex]
The canoeist's rate cannot be negative, then his rate in still water is 7 mph.
