Question 277019
Stephanie took her kayak to the Kaweah River, which flows downstream at a rate of 2 kilometers per hour. She paddled 15 km upstream, and then paddles downstream to her starting point. If this round-trip took a total of 4 hours, find the speed that Stephanie can paddle in still water


Let her speed in still water be x

upstream her speed will be x-2 kph

time taken upstream = x/x-2

time taken down stream is x/x+2

15/x-2 +15/x+2= 4 hours

15(x+2)+15(x-2)=4(x+2)(x-2) 

15x+30+15x-30=4(x+2)(x-2)
30x=4x^2-16

4x^2-30x-16=0

2x^2-15x-8=0
2x^2-16x+x-8=0

2x(x-8)+1(x-8)=0

(x-8)(2x+1)=0
x=8  rate in still water