SOLUTION: Solve Navigation. The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a barge to travel 24 mi upriver and then return in a total of 5 h

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Solve Navigation. The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a barge to travel 24 mi upriver and then return in a total of 5 h      Log On


   

Question 482438: Solve Navigation. The current in a typical Mississippi River shipping route flows at a rate of 4 mph. In order for a barge to travel 24 mi upriver and then return in a total of 5 hr, approximately how fast must the barge be able to travel in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The current in a typical Mississippi River shipping route flows at a rate of 4 mph.
In order for a barge to travel 24 mi upriver and then return in a total of 5 hr,
approximately how fast must the barge be able to travel in still water?
:
Let s = speed in still water
then
(s-4) = effective speed up-river
and
(s+4) = effective speed down-river
:
Write a time equation; time = dist/speed
:
Time up + time down = 5 hrs
24%2F%28%28s-4%29%29 + 24%2F%28%28s%2B4%29%29 = 5
:
Multiply by (s-4)(x+4), results
24(s+4) + 24(s-4) = 5(s+4)(s-4)
:
24s + 96 + 24s - 96 = 5(s^2-16)
:
48s = 5s^2 - 80
A quadratic equation
5s^2 - 48s - 80 = 0
Use the quadratic formula to find s; a=5; b=-48; c=-80
You should get a positive solution: s = 11.05 mph in still water