Problema Solution
The speed of a stream is 2mph. A boat travels 6 miles upstream in the same time it takes to travel 10 miles downstream. What is the speed of the boat in still water?
Answer provided by our tutors
let
v = the speed of the boat in still water, v>0
c = 2 mph speed of a stream
d1 = 6 miles the distance he travels upstream
d1 = 10 miles the distance he travels downstream
the time of the travel upstream = the time of the travel downstream
downstream speed: v + c = v + 2
upstream speed: v - c = v - 2
since speed = distance/time we have time = distance/speed and the time of the travel upstream = the time of the travel downstream
t = d1/(v - c)
t = 6/(v - 2)
t = d2/(v + c)
t = 10/(v + 2)
by solving the equation
6/(v - 2) = 10/(v + 2)
we find
v = 8 mph the speed of the boat in still water
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