a motorboat traveled for 2 hours with an 8km/h current. the return trip against the same current took 3 hours. find the speed of the motorboat in still water.

Let x be the unknown speed, y the unknown distance.

distance equals speed times time.

"With" an 8kph current means our speed is x+8. 2 hours with an 8 kph current gets is a distance y:

y = 2 (x + 8)

Against the current, speed x-8, took 3 hours to go y:

y = 3 (x-8)

Equating,

2 (x+8) = 3 (x-8)

2x + 16 = 3x - 24

40 = x

Answer: 40 km/h

Check: 2 (40+8) = 96 km. 3 (40-8) = 3 (32) = 96 km. Equal, good.