Rate of speed question. ( Rowing with and against current )?

The current is 2 MPH.

You need to find 2 numbers such that :

(8 - x) t = (8+ x)(16 - t)

I found that 2 works here by an educated guess.

(8 - 2) 10 = (8 + 2) 6

and 10 + 6 = 16

Well to start you already now the speed the canoist can travel in still water! This should help you. Now, immagine your self in a pool... there you would have a speed in still water (top speed). Now imagine you go into a river and you try to swim down-stream (with the current). The speed that someone at the shore will see you swimming will be your speed (top speed) + the speed of the current, since it is pushing you faster. This 'total' speed (with current) is what you will need to use to compute distances. In the event that you will be swimming against the stream then the current will slow you down: your speed - speed of current. This 'total' speed (counter-current) will be used to compute distances.

You can start considering the trip up-stream and then the trip down-stream. Also, distance up = speed up. time up. Or distance down = speed down. time down. These speeds will refer to the 'total' speed on each leg.

Hope this helps. Good luck!

Not enough information to solve. How far did he get going up stream and in what portion of the 16 hours did it take. Then you could compute the current. As it stands, he could have done it on calm water, but we do not know the other variables.