Help solving please.

Question

Bobby paddle Tuscany in Tranquil Waters for three miles per hour for 2 hours. He then encounters a current in his Direction and paddle current for 1 hour to arrive at his destination. Returning, he paddles Upstream against the current twice as strong for one hour. If he has 9 more miles to go to reach his destination, what is the speed of the current?

Answer 1

Let x = speed of current downstream

     2x = speed of current upstream

     2 mph = paddling speed in still water

 

Distance = (Rate)(Time)

 

Speed downstream (with current) = x + 2

Speed upstream (against current) = 2 - 2x

 

Distance downstream = (3)(2) + (x+2)(1) = x + 8

Distance upstream = (2-2x)(1) + 9 = 11 - 2x

 

Distance downstream = Distance upstream

 

                      x + 8 = 11 - 2x

 

                           3x = 3

 

                             x = 1 mph

 

The downstream current is 1 mph and the current upstream is 2 mph.