SOLUTION: I have searched everywhere reading everything... I do not know how to turn this problem into a quadratic equation. Sammy takes 5 hours longer to complete 300 lines of code than Mar

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I have searched everywhere reading everything... I do not know how to turn this problem into a quadratic equation. Sammy takes 5 hours longer to complete 300 lines of code than Mar      Log On


   

Question 277656: I have searched everywhere reading everything... I do not know how to turn this problem into a quadratic equation. 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
Found 2 solutions by stanbon, edjones:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
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
-------------------------------
Let Martin time = x hr/job ; then Martin rate = 1/x job/hr
----------------------
Sammy time = (x+5)hr/job; Sammy rate = 1/(x+5) job/hr
---------------------------
Together time = 6 hr/job ; Together rate = 1/6 job/hr
---------------------------
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
-----------------------------------
Lines per Hour?
Martin rate = (1/10)(300) = 30 lines per hour
Sammy rate = (1/15)(300) = 20 lines per hour
=================================================
Cheers,
Stan H.

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let s=hrs sammy takes and m=hrs martin takes
s=m+5
in 1 hr martin gets 1/m of the job done and sammy gets 1/(m+5) done.
1/m + 1/(m+5) = 1/6
6(m+5)+6m=m(m+5)
6m+30+6m=m^2+5m
m^2-7m-30=0
(m-10)(m+3)=0
m=10 hrs
s=15 hrs
.
Ed