SOLUTION: In two hpurs, a motorboat can travel 8 miles down a river and return 4 miles back. If the river flows at a rate of 2 mph, what is the rate of the boat in still water?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: In two hpurs, a motorboat can travel 8 miles down a river and return 4 miles back. If the river flows at a rate of 2 mph, what is the rate of the boat in still water?      Log On


   

Question 633475: In two hpurs, a motorboat can travel 8 miles down a river and return 4 miles back. If the river flows at a rate of 2 mph, what is the rate of the boat in still water?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
In two hours, a motorboat can travel 8 miles down a river and return 4 miles back.
If the river flows at a rate of 2 mph, what is the rate of the boat in still water?
:
Let s = boat speed in still water
then
(s+2) = effective speed down river
and
(s-2) = effective speed up river
:
Write a time equation: time = dist/speed
;
Down riv time + up riv time = 2 hrs
8%2F%28s%2B2%29 + 4%2F%28s-2%29 = 2
Multiply by (s-2)(s+2) to get rid of the denominators, results:
8(s-2) + 4(s+2) = 2(s-2)(s+2)
:
8s - 16 + 4s + 8 = 2(s^2 - 4)
12s - 8 = 2s^2 - 8
add 8 to both sides
12s = 2s^2
0 = 2s^2 - 12s
0 = 2s(s - 6)
The reasonable solution
s = 6 mph is the speed in still water
:
:
See if that checks out find the time each way
8/(6+2) = 1 hr
4/(6-2) = 1 hr
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total time 2 hrs