Question

Annette's paddleboat travels 2 km/hour in still water. the boat is paddled 4 km downstream in the same time that it takes to go 1 km upstream. what is the speed of the river's current?

Answer 1

the boat travels 2km/hr without any current

let's let the speed of the current be c

downstream speed: 2 + c (the boat is sped up by the current)
upstream speed: 2 - c (the boat is fighting the current)

in general, d = st (distance = speed * time)
solving for t: t = d/s

it says that the upstream time for 4km is the same as the downstream speed for 1km

so setting up the time equation for both:

t = d/s = 4/(2 - c) = 1/(2 + c)
solve for c