SOLUTION: A motorboat heads upstream a distance of 24 miles on a river with current running 3 miles per hour. The trip up and back takes 6 hours. Assuming the motorboat maintained a constant
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Question 739431: A motorboat heads upstream a distance of 24 miles on a river with current running 3 miles per hour. The trip up and back takes 6 hours. Assuming the motorboat maintained a constant speed relative to the water, what was it's speed?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The speed of the boat going upstream is
mi/hr
The speed of the boat going downstream is
mi/hr
where = the boat's speed in still water
Let = the time in hrs for the boat to go upstream
-----------------
Going upstream:
(1)
Going downstream:
(2)
--------------------------
(2)
(2)
and
(1)
-------------------
Substitute (1) into (2)
(2)
(2)
(2)
Substitute this back into (1)
(1)
(1)
(1)
(1) ( by inspection )
( can't use )
The boats speed is 9 mi/hr without a current
check:
(1)
(1)
(1) hrs
and
(2)
(2)
(2)
(2)
(2)
(2) hrs
OK
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