Problema Solution
a boat goes 350 miles downstream in the same time it can go 300 miles upstream. the speed of the boat current is 7 miles per hour. find the speed of the boat at still water.
Answer provided by our tutors
let
v = the speed of the boat in still water, v>0
c = 7 mph speed of the stream
d1 = 350 miles the distance he travels upstream
d2 = 300 miles the distance he travels downstream
the time of the travel upstream = the time of the travel downstream
downstream speed: v + c
upstream speed: v - c
since speed = distance/time we have time = distance/speed and the time of the travel upstream = the time of the travel downstream
upstream travel
t = d1/(v - c)
t = 300/(v - 7)
downstream travel
t = d2/(v + c)
t = 350/(v + 7)
the time of the travel upstream = the time of the travel downstream
300/(v - 7) = 350/(v + 7)
by solving the equation we find
6/(v - 2) = 10/(v + 2)
we find
v = 91 mph
click here to see the step by step solution of the equation
the speed of the boat in still water is 91 miles per hour.