a boat took 4 hours to make a trip downstream with a current of 6 km/h
the return trip against the same current took 10 hours
how far did the boat travel?
how do you find the solution?
Call the rate of the boat in still water, R
And when the boat is traveling with the current, its rate is (R + 6) km/ hr
So... Rate * Time = Total Distance
( R + 6 ) * 4 = D (1)
And Distance / Rate = Time (in hours)
Note that when the boat goes against the current, that its rate is being slowed by the current...so its rate is (R - 6)...so we have
D / ( R - 6) = 10 (2)
Sub (1) into (2)
(R + 6) * 4 / (R - 6) = 10 simplify
(R + 6) * 4 = 10 (R - 6)
4R + 24 = 10 R - 60 subtract 4R from both sides, add 60 to both sides
84 = 6R divide both sides by 6
14 = R ( the rate in still water is 14 km/hr)
To find the distance, plug 14 into (1)
(14 + 6) * 4 = D
20 * 4 = 80
So...the distance is 80 km (one way)