SOLUTION: A motorboat maintains a constant speed of 15 mph relative to the water in a river. The boat went 10 miles upstream and back in a total of 1.5 hours. What is the speed of the curren

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Question 903301: A motorboat maintains a constant speed of 15 mph relative to the water in a river. The boat went 10 miles upstream and back in a total of 1.5 hours. What is the speed of the current (in mph)?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
boat speed = 15 km/h
current speed = x km/h

against current = 15 - x
with current = 15 + x

Total distance = 10 miles Total Time= 1.50 hours
Time upstream + time downstream = 1.5 hours

10 /( 15 - x )+ 10 /( 15 + x )= 1.5
10 ( 15 + x )+ 10 ( 15 - x )= 1.50 ( 225 - 1 X^2 )
150 + 10 x + 150 -10 x = 337.5 - 1.5 X^2
300 - -337.5 = -1.5 X^2
-37.5 = -1.5 X^2
-1.5 X^2= -37.5
X^2 = 25
X = +/- 5
speed of current = 5 mph