Question 277656
Sammy takes 5 hours longer to complete 300 lines of code than Martin. 
Together Sammy and Martin can complete the code in 6 hours. 
How long does it take each programmer to complete the code if they complete on their own. 
At what speed is each programming lines per hour
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Let Martin time = x hr/job ; then Martin rate = 1/x job/hr
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Sammy time = (x+5)hr/job; Sammy rate = 1/(x+5) job/hr
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Together time = 6 hr/job ; Together rate = 1/6 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x+5) = 1/6
Multiply thru by 6x(x+5) to get:
6(x+5) + 6x = x(x+5)
12x + 30 = x^2 + 5x
x^2-7x-30 = 0
Factor:
(x-10)(x+3) = 9
Positive solution:
x = 10 hrs (Martin's time to do the job alone); his rate = 1/10 job/hr
x+5 = 15 hrs (Sammy's time to do the job alone); his rate = 1/15 job/hr
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Lines per Hour?
Martin rate = (1/10)(300) = 30 lines per hour
Sammy rate = (1/15)(300) = 20 lines per hour
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Cheers,
Stan H.