Translate to a system of equations and solve
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.

40 km/h

Step-by-step explanation:

Let the speed of motorboat in still water = x km/h

Speed of current = 8 km/h

When moving with the current, the relative speed is = (x + 8) km/h

When moving against the current, the relative speed = (x - 8) km/h

Travelling against the current will take longer. So, it took 3 hours to travel against the current and 2 hours to travel in the direction of the current.

The distance traveled in each case remains the same.

Since, Distance = Speed x Time, we can write:

Distance traveled with current = Distance traveled against current

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

2x + 16 = 3x - 24

16 + 24 = 3x - 2x

x = 40 km/h

Thus, the speed of motorboat in still water will be 40 km/h