How do you find the speed of the rowboat in still water if it took 3 hours to row a boat 18 km against the current and the return trip with the current took 1 1/2 hours?

Mar 25, 2015

Lets call the speeds ${v}_{c}$ and ${v}_{r}$

Then the speed out $= {v}_{r} - {v}_{c} = \frac{18}{3} = 6 k m / h$

Return trip speed $= {v}_{r} + {v}_{c} = \frac{18}{1.5} = 12 k m / h$

If we add these two equations, the ${v}_{c}$'s cancel out:

$2 \cdot {v}_{r} = 18 \to {v}_{r} = 9 k m / h$ and that's your answer

It is easy to see that ${v}_{c} = 3 k m / h$ in case that's the next question.

Mar 25, 2015

Average speed = 8km/hr

Total distance = 18 x 2 = 36km

Total time = 3 + 1.5 = 4.5 hr

Average speed = dist/time = 36/4.5 = 8km/hr