SOLUTION: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her
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Question 80880: Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Debbie traveled by boat 5 miles upstream to fish in her favorite spot. Because of the 4-mph current, it took her 20 minutes longer to get there than to return. How fast will her boat go in still water?
:
let x = boat speed in still water
Then:
(x-4) = speed up-stream
and
(x+4) = speed down stream
:
Since we are dealing in mph, change 20 min to hrs. 20/60 = 1/3 hr
:
Write a time equation; Time = dist/speed
:
Time down-stream + 1/3 hr = time upstream
+ =
:
Multiply equation by 3(x+4)(x-4) to get rid of the denominators, you then have;
:
15(x-4) + (x+4)(x-4) = 15(x+4)
:
15x - 60 + x^2 - 16 = 15x + 60; multiplied what's inside the brackets
:
x^2 + 15x - 15x = + 60 + 60 + 16; x's on the left, numbers on the right
:
x^2 = 136
:
x =
:
x = 11.66 mph in still water
:
Check solution by finding the times
Speed up = 7.66, speed down = 15.66
:
5/7.66 = .65 hr
5/15.66 = .32
---------------
subtract= .33 hr difference, check our solution of x = 11.66
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