Problema Solution
In still water, a boat averages 14 miles per hour. It takes the same amount of time to travel 22 miles downstream, with the current, as it does 11 miles upstream, against the current. What is the rate of the water's current?
Answer provided by our tutors
let
v = 14 mph the speed of the boat in still water (no current)
c = the water's current
the speed upstream is: v - c = 14 - c
the speed downstream is: v + c = 14 + c
since speed = distance/time => time = distance/speed
it takes the same amount of time to travel 22 miles downstream, with the current, as it does 11 miles upstream, against the current
22/(v + c) = 11/(v - c)
22/(14 + c) = 11/(14 - c)
by solving we find
c = 4.67 mph
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the rate of water's current is 4.67 mph.