Q 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?

Okay... First I drew a diagram, and defined some variables...

Michael's rowing velocity in still water

Velocity of the current in the river

Time taken for Michael to cover x km downstream

Time taken for Michael to cover x km upstream

Time taken for Tom to cover 1 km

We know . We also know that

Also, the velocity of the current will affect Michael's rowing velocity. So, Michael's speed downstream will be , and when he turns around and moves upstream.

So, I got three equations, as follows:

For the third equation, I used the fact that equals the time taken for Tom to cover 1 km. So:

There are too many variables... How do I proceed? Or am I on the wrong track... and there's an easier way to get this done?

Help!

Thanks.

ILoveMaths07.