Question 335785
The first programmer,Sammy,grossed $535 in 1 week by working 48 hours. The second programmer, Matin, grossed $587 in 1 week by working 52 hours. Time-and-a-half is paid for all hours worked in excess of 40 hours. Which programmer earns more per hour. I have to use a linear equation to do this problem.
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Let Sammy's hourly rate be "S"
Let Martin's hourly rate = "M"
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Equations:
Sammy Eq: 40S + (S/2)8 = 535 dollars
40S+4S = 535
44S = 535
S = $12.16 per hour (Sammy's hourly rate)
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Martin Eq;40M + (M/2)12 = 587
40M + 6M = 587
46M = 587
M = $12.76 per hour (Martin's hourly rate)
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Sammy takes 5 hours longer to complete 300 lines of code than Martin. Toghether, Sammy and Martin can complete the code in 6 hours.
Sammy DATA:
time = x+5 hr/job ; rate = 1/(x+5) job/hr
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Martin DATA:
time = x hr/job ; rate = 1/x job/hr
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Together DATA:
time = 6 hr/job ; rate = 1/6 job/hr
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Equation:
rate + rate = together rate
1/(x+5) + 1/x = 1/6
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Multiply thru by 6x(x+5)
6x + 6(x+5) = x(x+5)
6x + 6x+30 = x^2+5x
12x + 30 = x^2+5x
x^2 - 7x - 30 = 0
Factor:
(x-10)(x+3) = 0
Positive solution:
x = 10 hrs (time required by Martin to do the job alone)
Martin's rate is 1/10 job/hr.
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x+5 = 15 hrs (time required by Sammy to do the job alone)
Sammy's rate is 1/15 job/hr.
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Cheers,
Stan H.
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Clearly explain the results showing the calculations of how long it takes each programmer to complete the code if he programs on his own. (hint:quadratic equation) and at what speed he is programming lines per hour