SOLUTION: A stream Flows at a rate of 5 mph. A boat travels 75 mi upstream and returns in a total of 8 hours. What is the speed of the boat in still water?

Question 172429: A stream Flows at a rate of 5 mph. A boat travels 75 mi upstream and returns in a total of 8 hours. What is the speed of the boat in still water?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A stream Flows at a rate of 5 mph. A boat travels 75 mi upstream and returns
in a total of 8 hours. What is the speed of the boat in still water?
:
Let s = boat speed in still water
then
(s-5) = speed upstream
and
(s+5) = speed down stream
:
Write a time equation: Time=
:
Time upstream + time downstream = 8 hours
+ = 8
:
Multiply equation by (s-5)(s+5)
(s-5)(s+5)* + (s-5)(s+5)* = 8(s-5)(s+5)
results
75(s+5) + 75(s-5) = 8(s^2 - 25)
:
75s + 375 + 75s - 375 = 8s^2 - 200
:
150s = 8s^2 - 200
:
Arrange as a quadratic equation
8s^2 - 150s - 200 = 0
:
Simplify divide equation by 2:
4s^2 - 75s - 100 = 0
Factors to:
(4s + 5)(s - 20) = 0
Positive solution:
s = +20 speed of boat in still water
:
:
Check the solution by finding the times of up and down streams
75/15 = 5 hrs
75/25 = 3 hrs
-------------
total = 8 hrs
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