SOLUTION: A motorboat takes 5 hours to travel 100 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the c

Question 1111941: A motorboat takes 5 hours to travel 100 km going upstream. The return trip takes 2 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
Rate of the boat still in water: ____ km/h
Rate of the current: _____ km/h
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let s = boat speed in still water
let c = rate of the current
then
(s+c) = effective speed downstream
and
(s-c) = effective speed upstream
:
A motorboat takes 5 hours to travel 100 km going upstream.
The return trip takes 2 hours going downstream.
Write a distance equation for each way. Dist = time *speed
5(s-c) = 100
2(s+c) = 100
simplify both equations, divide the 1st one by 5, the 2nd one by 2
s - c = 20
s + c = 50
-------------Addition eliminates c find s
2s + 0 = 70
s = 70/2
s = 35 km/hr in still water
and using the equation s + c = 50
35 + c = 50
c = 50 - 35
c = 15 km/hr is the current
:
:
check in the 1st original equation
5(35 - 15) = 100

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