SOLUTION: A motorboat maintained a constant speed of 15 mph relative to the water in going 10 miles upstream and then returning. The total time for this trip was 1.5 hours. Use this info to

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Question 882550: A motorboat maintained a constant speed of 15 mph relative to the water in going 10 miles upstream and then returning. The total time for this trip was 1.5 hours. Use this info to find the speed of the current.
*PLEASE* help explain how I figure this out!
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website!
A motorboat maintained a constant speed of 15 mph relative to the water in going 10 miles upstream and then returning. The total time for this trip was 1.5 hours. Use this info to find the speed of the current.
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let x=speed of current
15+x=speed of boat downstream
15-x=speed of boat upstream
travel time=distance/speed
total travel time=travel time upstream+travel time downstream
1.5=10/(15-x)+10/(15+x)
lcd:(15-x)(15+x)
1.5*(15-x)(15+x)=10(15+x)+10(15-x)
1.5(15^2-x^2)=150+10x+150-10x
1.5(225-x^2)=300
(225-x^2)=200
x^2=25
x=�5
speed of current=5 mph