Word Problem?

Question

A boat goes downstream a distance of 5 km in 15 min, but it takes 20 min for the return trip. Find the rate of the boat in still water and the rate of the current.

Answer 1

Let the rate of the boat in still water = B km/min and the rate of the current = C km/min.

Then, net rate of boat while going upstream = (B - C) km/min and net rate of boat while going downstream = (B + C) km/min.

Then, B - C = 5/20 = 1/4 _______ (1)
and B + C = 5/15 = 1/3 ________ (2)

Adding both sides of equations (1) and (2)
2B = 1/4 + 1/3 = 7/12
or B = 7/24

Subtracting both sides of equation (1) from that of equation (2)
2C = 1/3 - 1/4 = 1/12
or C = 1/24

Thus the rate of the boat in still water and the rate of the current are 7/24 km/min i.e. 17.5 kmph and 1/24 km/min i.e. 2.5 kmph respectively.

Answer 2

The boat goes downstream at 20kph (kilometers per hour) but goes upstream at 15 kph. So the river must be going at 2.5 kph. In still water the boat would go 17.5 kph.