Maths
posted by Maybel on .
Tom was floating down the river on a raft when, 1km 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 when 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?

Where was Tom when Michael started rowing? He must have been farther upstream at the time. I will assume Tom was one km upstream when Michael started rowing.
Let v = the river speed and V = 10v be Michael's speed in still water.
Michael rows downstream at a land speed v + V = 11 v and upstream at a land speed of Vv = 9 v. Tom travels at speed v (by floating)
Let T be the time they both are on the water between when Michael starts and finishes rowing.
Let t be the time Micheal rows downstream; Tt is the time he rows upstream
v T = 1 km
11 v t = 9 v (Tt)= 9  9 vt
20 vt = 9
vt = 0.45 km
So Tom floated 0.45 km while Micheal rowed downstream and 0.55 km while he rowed upstream. Since Micheal rowed downstream 11 times faster than Tom floated, he would have travelled 11*0.45 = 4.95 km in that time 
dfh