SOLUTION: I am having trouble creating equations for solving this proportion. Frank and Dana take turns mowing a field for Mr. Thibodeaux. It takes Dana four hours to do the job, and it

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Question 657189: I am having trouble creating equations for solving this proportion.
Frank and Dana take turns mowing a field for Mr. Thibodeaux. It takes Dana four hours to do the job, and it takes Frank six hours. One day Mr. Thibodeaux borrows an extra tractor and hires the two to work together to mow the field for a total of $43.50. Frank works for two-and-a-half hours then leaves; Dana finishes the job alone.
a) How should they split the money if they are paid the same hourly rate?
b) How should they split the money if they are paid by the portion of the field that they mowed?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Frank and Dana take turns mowing a field for Mr. Thibodeaux. It takes Dana four hours to do the job, and it takes Frank six hours. One day Mr. Thibodeaux borrows an extra tractor and hires the two to work together to mow the field for a total of $43.50. Frank works for two-and-a-half hours then leaves; Dana finishes the job alone.
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Dana rate: 1/4 job per hour
Frank rate: 1/6 job per hour
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Equation:
(1/6)(5/2 hrs) + (1/4 *x hrs) = 1 job
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(5/12) + (x/4) = 1
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5 + 3x = 12
3x = 7
x = 7/3 hr
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Frank worked for 2 1/2 hrs
Dana worked for 2 1/3 hrs

a) How should they split the money if they are paid the same hourly rate?
Frank Pay: (5/2)/[(5/2)+(7/3)]*43.50 = (5/2)/(29/6)43.50 = $21.98
Dana Pay = 43.50-21.98 = $21.52
b) How should they split the money if they are paid by the portion of the field that they mowed?
Frank Pay: (5/2)(1/6) = 5/12 of the field: (5/12)(43.50 = $18.13
Dana Pay: 43.50-18.13 = $25.37
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Cheers,
Stan H.