SOLUTION: A small motorboat travels 15 mph in still water. It takes 1 hour longer to travel 72 miles going upstream than it does going downstream. Find the speed of the current.

Question 1056878: A small motorboat travels 15 mph in still water. It takes 1 hour longer to travel 72 miles going upstream than it does going downstream. Find the speed of the current.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
velocity* time=distance
upstream is 15-x
downstream is 15+x, where x is the current speed.
15+x*time1=72
time1=72/(15+x)
15-x*time2=72
time2=72/(15-x)
time 2 is 1 more than time 1
so 72/(15-x)-1=72/(15+x)
Multiply everything by (15+x)(15-x) to clear fractions
72(15+x)-(225-x^2)=72(15-x)
1080+72x-225+x^2=1080-72x. The 1080 cancel
x^2+144x-225=0
x=(1/2)(-144+ sqrt (20736+900);sqrt (21636)=147.09; x=(1/2)3.09, using only the positive root.
x=1.545 mph current. ANSWER
Upstream is 13.455 mph and it takes 5.35 hours
Downstream is 16.545 mph and it takes 4.35 hours
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