Alvin paddled for 5 hours with a 2​-km/h current to reach a campsite. The return trip against the same current took 7 hours. Find the speed of the boat in still water.

Answer 1

As I paddle downstream, the current adds to my speed. As I paddle upstream, the current subtracts from my speed. If I paddle 5 km/h upstream in a 5 km/h current, I sit still, but I go 10 km/h downstream.

d = rt and the distances are the same.

5(r + 2) = 7(r - 2)

5r + 10 = 7r - 14

-2r = -24

r = 12 km/h

Answer 2

5 hours with 2 kph current downstream

7 hours with 2 kph current upstream

d=rt where distance = rate of speed times time

d= (x+2)5 = (x-2)7

5x+ 10 = 7x -14

2x = 24

x = 12 kph in still water

12-2 = 10 times 7 = 70

12+2 - 14 times 5 = 70