SOLUTION: 3.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 s

          SPEED      TIME           DISTANCE

DOWN       8+c         15/(8+c)         15

UP         8-c         15/(8-c)         15

TOTAL                   4

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 !