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?
:
Let s = boat speed in still water
then
(s-5) = speed upstream
and
(s+5) = speed down stream
:
Write a time equation: Time= {{{dist/speed}}}
:
Time upstream + time downstream = 8 hours
{{{75/((s-5))}}} + {{{75/((s+5))}}} = 8
:
Multiply equation by (s-5)(s+5)
(s-5)(s+5)*{{{75/((s-5))}}} + (s-5)(s+5)*{{{75/((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