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?

OfficialBubbleTanks
Jun 27, 2018

#1**+1 **

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)

CPhill
Jun 27, 2018