SOLUTION: Alfred, Mindy, and Casey can mow their lawn in 60 minutes if they work together. If it takes Alfred twice as long as Mindy and Casey 10 minutes more than Mindy, how long would it t

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Question 896878: Alfred, Mindy, and Casey can mow their lawn in 60 minutes if they work together. If it takes Alfred twice as long as Mindy and Casey 10 minutes more than Mindy, how long would it take each to mow the lawn alone? (Round answers to nearest whole minute.)
I tried organizing the information in a chart and in the time column I have Alfred-2m, Mindy-m, Casey-m+10, and together 60m.
Found 3 solutions by josgarithmetic, richwmiller, stanbon:
Answer by josgarithmetic(39800) About Me  (Show Source):
You can put this solution on YOUR website!
Try assigning a variable to one of the times for one of the workers to do 1 lawn-mow job. Mindy seems to be best for this time variable assignment.

Alfred, 1%2F%282x%29
Mindy, 1%2Fx
Casey, 1%2F%28x%2B10%29
The time unit for x is MINUTES.

The three working all at once do the job in 60 minutes, is the sum of their individual rates.
highlight_green%281%2F%282x%29%2B1%2Fx%2B1%2F%28x%2B10%29=1%2F60%29.
Just a bit of algebra to solve for x.

Note very carefully, the simplest common denominator is 60%2Ax%2A%28x%2B10%29.
Be sure you know why, and how.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
1/a+1/m+1/c=1/60
a=2m
c=m+10
1/(2m)+1/m+1/(m+10)=1/60
a=292.315, c=156.158, m=146.158
rounded
a=292, c=156, m=146
check
60/292+60/156+60/146=950/949
close enough
ok

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Alfred, Mindy, and Casey can mow their lawn in 60 minutes if they work together. If it takes Alfred twice as long as Mindy, and Casey 10 minutes more than Mindy, how long would it take each to mow the lawn alone? (Round answers to nearest whole minute.)
I tried organizing the information in a chart and in the time column I have Alfred-2m, Mindy-m, Casey-m+10, and together 60m.
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Together DATA:: time = 60 min/job ; rate = 1/60 job/min
Mindy DATA:: time = x min/job ; rate = 1/x job/min
Alfred DATA:: time = 2x min/job ; rate = 1/(2x) job/min
Casey DATA:: time = x+10 min/job ; rate = 1/(x+10) job/min
----------------------------------------
Equation::
1/x + 1/(2x) + 1/(x+10) = 1/60
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Multiply thru by 60x(x+10) to get::
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60(x+10) + 30(x+10) + 60x = x(x+10)
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60x + 600 + 30x + 300 + 60x = x^2 + 10x
--------
150x + 900 = x^2 + 10x
---------------------------
x^2 - 140x - 900 = 0
Mindy time::x = 146.16 miinutes
Alfred time:: 2x = 292.32 minutes
Casey time:: x + 10 = 156.16 minutes
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Cheers,
Stan H.
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