SOLUTION: I typed the question incorrect the first time, SORRY... Together,it takes John and Deb 2 hr 55 min to sort recyclables. Alone, John would require 2 more hrs than Deb. How long w

Algebra ->  Expressions-with-variables -> SOLUTION: I typed the question incorrect the first time, SORRY... Together,it takes John and Deb 2 hr 55 min to sort recyclables. Alone, John would require 2 more hrs than Deb. How long w      Log On


   

Question 186746: I typed the question incorrect the first time, SORRY...
Together,it takes John and Deb 2 hr 55 min to sort recyclables. Alone, John would require 2 more hrs than Deb. How long would it take Deb to do the job alone?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Together,it takes John and Deb 2 hr 55 min to sort recyclables.
Alone, John would require 2 more hrs than Deb.
How long would it take Deb to do the job alone?
:
It might be easier to do this in minutes:
Together: 2(60) + 55 = 175 min
:
Let t = time for D to do it alone
then
(t+120) = J's time alone:
;
A typical shared work equation (let the completed job = 1):
175%2Ft + 175%2F%28t%2B120%29 = 1
Multiply equation by t(t+120) to get rid of the denominators
175(t+120) + 175t = t(t+120)
:
175t + 21000 + 175t = t^2 + 120t
;
350t + 21000 = t^2 + 120t
:
0 = t^2 + 120t - 350t - 21000
a quadratic equation:
t^2 - 230t - 21000 = 0
Factor this to:
(t-300)(t+70) = 0
the positive solution:
t = 300 minutes or 5 hrs is D's time alone
:
:
Check solution:
(175/300) + (175/420) = 1