SOLUTION: a boat traveled 135 mules downstream and back. The trip downstream took 5 hours and the return trip took 9 hours. If the speed of the current is 6 mph, what is the speed of the b

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Question 571335: a boat traveled 135 mules downstream and back. The trip downstream took 5 hours and the return trip took 9 hours. If the speed of the current is 6 mph, what is the speed 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!
a boat traveled 135 mules downstream and back.
The trip downstream took 5 hours and the return trip took 9 hours.
If the speed of the current is 6 mph, what is the speed of the boat in still water?
:
Let s = speed of the boat instill water
then
(s-6) = effective speed upstream
(s+6) = effective speed downstream
:
Write a time equation: time = dist/speed
:
Upstr time + downstr time = 9 hrs
135%2F%28%28s-6%29%29 + 135%2F%28%28s%2B6%29%29 = 9
Multiply by (s-6)(s+6), results:
135(s+6) + 135(s-6) = 9(s+6)(s-6)
:
135s + 810 + 135s - 810 = 9(s^2-36)
270s = 9s^2 - 324
0 = 9s^2 - 270s - 324
Simplify, divide by 9
s^2 - 30s - 36 = 0
Solve this using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
In this equation; x=s; a=1; b=-30; c=-36
s+=+%28-%28-30%29+%2B-+sqrt%28-30%5E2-4%2A1%2A-36+%29%29%2F%282%2A1%29+
:
s+=+%2830+%2B-+sqrt%28900-%28-144%29+%29%29%2F2+
:
s+=+%2830+%2B-+sqrt%281044%29%29%2F2+
Two solutions but only this one is reasonable
s+=+%2830+%2B+32.311%29%2F2+
s = 62.311%2F2
s = 31.156 mph in still water
:
:
See if this checks out
135/37.156 = 3.63 hrs
135/25.156 = 5.37
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total time: 9.00 hrs