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Dong rowed his boat 15 km downstream and returned back 15 km upstream.
It took him a total of 4 hours rowing his boat.
If he can row the boat in 8 km in still water what is the speed of the current in the stream?
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His effective speed rowing downstream is (8+x) kilometers per hour.
His time rowing 15 km downstream is hours.
His effective speed rowing upstream is (8-x) kilometers per hour.
His time rowing 15 km upstream is hours.
The total time for the entire round trip downstream and upstream is + hours.
According to the problem, the total time is 4 hours. It gives you this "time" equation
+ = 4.
At this point, the setup is complete, and your task is to solve this equation to find x.
For it, multiply both sides of the equation by (8+x)*(8-x) = 64-x^2. You will get
15*(8-x) + 15*(8+x) = 4*(64-x^2)
120 - 15x + 120 + 15x = 256 - 4x^2
240 = 256 - 4x^2
4x^2 = 256 - 240
4x^2 = 16
x^2 = 16/4 = 4
x = = 2.
Thus the problem is just solved, and the ANSWER is: the rate of the current is 2 km per hour.
CHECK. The rate downstream is 8+2 = 10 km/h; the time rowing downstream is = 1.5 hours.
The rate upstream is 8-2 = km/h; the time rowing upstream is = 2.5 hours.
The total time traveling is 2.5 + 1.5 hours = 4 hours: ! correct !
Solved and thoroughly explained.