Problema Solution
A motorboat travels 9 miles upstream,against a current of 4 miles per hour,and returns 9 miles downstream helped by the same current. The total travel time is 3 hours. Find the speed of the motorboat in still water.
Answer provided by our tutors
let
v = the rate of the boat in still water, v>0
c = 4 mph the rate of the current
d1 = 9 mi the distance traveled upstream
d2 = 9 mi the distance traveled downstream
t = 3 hr the total time of the travel
the canoe's speed downstream: v + c = v + 4
the canoe's speed upstream: v - c = v - 4
since speed = distance/time => time = distance/speed
d1/(v - 4) + d2/(v + 4) = t
9/(v - 4) + 9/(v + 4) = 3
by solving we find
v = 8 mph
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the speed of the motorboat in still water is 8 miles per hour.