SOLUTION: The Stemsell River flows at a rate of 4Km/h. In order for a boat to travel 33.6 km upriver and then return in a total of 8 hr, how fast must the boat travel in still water?

Question 372437: The Stemsell River flows at a rate of 4Km/h. In order for a boat to travel 33.6 km upriver and then return in a total of 8 hr, how fast must the boat travel in still water?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The Stemsell River flows at a rate of 4Km/h.
In order for a boat to travel 33.6 km upriver and then return in a total of 8 hr,
how fast must the boat travel in still water?
:
Let s = boat speed in still water
then
(s-4) = effective speed upstream
and
(s+4) = effective speed downstream
:
Write a time equation: time = dist/speed
:
time upstream + time downstream = 8 hrs
+ = 8
:
multiply by (s-4)(s+4), to clear the denominator, results
33.6(s+4) + 33.6(s-4) = 8(s+4)(s-4)
:
33.6s + 134.4 + 33.6s - 134.4 = 8(s^2 - 16)
:
67.2s = 8s^2 - 128
:
A quadratic equation
8s^2 - 67.2s - 128 = 0
:
simplify, divide by 8
s^2 - 8.4s - 16
:
This will factor to:
(x+1.6)(x-10) = 0
:
positive solution is what we want here:
s = 10 km/hr in still water
:
:
Check this, find the time of each trip
33.6/6 = 5.6 hrs
33.6/14= 2.4 hrs
----------------
total time 8 hrs
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