Problema Solution
If a boat can do 10 miles per hour in still water and takes the same time to go 12 miles up stream as 15 miles down stream find the speed of the current.
Answer provided by our tutors
let
v = 10 mph the rate of the boat in still water
d1 = 15 mi the distance downstream
d2 = 12 mi the distance upstream
t = the time of the travel upstream = the time of the travel downstream
c = the rate of the water's current
since rate = distance/time we have
the rate of the boat traveling downstream is: v + c
v + c = d1/t
10 + c = 15/t
t = 15/(10 + c)
the rate of the boat traveling upstream is: v - c
v - c = d2/t
10 - c = 12/t
plug t = 15/(10 + c) into the last equation
10 - c = 12/(15/(10 + c))
by solving we find
c = 10/9 mph
c = 1.11 mph
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the speed of the current is 1.11 mph.