Originally Posted by

**paulfr2**
Two equations can describe the given problem,

1/ one for swimming upstream; u = [ x - c ] 1/4

x = swimmers rate, c = current rate, 1/4 hr = 15 min

2/ one for swimming downstream; d = [ x + c ] 1/4

You seem to be assuming that the swimmer took the same time to swim upstream as downstream; that is not correct.

Suppose the swimmer’ speed in still water is

and that the speed of the current is

The distance covered by the swimmer going upstream is

and the raft will have drifted downstream a distance of

As the swimmer heads back, the time taken to cover the distance back to the bridge is

and so during this time the raft would have drifted a further

downstream. Now suppose

is the time taken for the swimmer to catch up with the raft from that point onwards. The swimmer would swim a distance of

while the raft would drift a further

downstream. Thus

From this, it should follow by patient algebraic manipulation that