Problema Solution
a boat can go 26 miles downstream in the same time it takes to go 6 miles upstream the rate of the water is 5 mph what is the rate of the boat
Answer provided by our tutors
let
v = the rate of the boat in still water, v>0
c = 5 mph the rate of the water
d1 = 6 mi the distance traveled upstream
d2 = 26 mi the distance traveled downstream
t = time of the travel in 1 direction
the boat's speed downstream: v + c = v + 5
the boats's speed upstream: v - c = v - 5
since speed = distance/time => time = distance/speed
d1/(v - c) = d2/(v + c)
6/(v - 5) = 26/(v + 5)
by solving we find
v = 8 mph
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the rate of the boat is 8 mph.