A boat cruises 36 miles against a 3 mph current and 36 miles back in the direction of the same current. The round trip takes 5 hours. What is the speed of the boat in the still water?

Question

use d=rt

Answer 1

Let V be the boat speed (with respect to water) and v=3 be the river speed.

36/(V+v) + 36(V-v)
=36/(V+3) + 36(V-3)
= 5 hours

Solve for V. You will get a quadratic equation. Take the positive root.

[36(V-3) + 36(V+3)]/(V^2-9) = 5
5V^2 -72V -45 = 0
(V-15)(5V +3) = 0

V = 15 mph

Answer 2

let speed of boat be x mph

time against current = 36/(x-3)
time with current = 36/(x+3)

solve
36/(x-3) + 36/(x+3) = 5

hint: multiply each term by (x+3)(x-3) to get a quadratic.