Euler maths problem 12 please help!?

Question

Tom was floating down the river on a raft when, 1 km lower down, Michael took to the water in a rowing boat. Michael rowed downstream at his fastest pace. Then he turned around and rowed back, arriving at his starting point just as Tom drifted by. If Michael's rowing speed in still water is ten times the speed of the current in the river, what distance had Michael covered before he turned his boat around?

Answer 1

let the speed of the current be x and y be the distance travelled by Mike.

in the total time taken by Micheal on his trip, Tom went 1 km. Tom was floating at a speed x. so, the time taken by Tom and the total time taken by Mike was 1/x.

while rowing downstream, Mike's speed was x + 10x = 11x.

while rowing upstream, Mike's speed was 10x - x = 9x.

time taken while rowing downstream = y / 11x

time taken while rowing upstream = y / 9x.

Total time = y / 11x + y / 9x

1/x = y/11x + y/9x

1/x = y/x ( 1/11 + 1/9 )

y ( 20/99 ) = 1

y = 99/20 = 4.95 km.

therefore, Micheal rowed 4.95 km downstream before he turned his boat around.