SOLUTION: Hi, I would like to say thank you in advance. My question is: A certain punch press requires 2 hours longer to stamp a box of parts than does a newer-model punch press. Af

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi, I would like to say thank you in advance. My question is: A certain punch press requires 2 hours longer to stamp a box of parts than does a newer-model punch press. Af      Log On


   

Question 1011086: Hi,
I would like to say thank you in advance.
My question is:
A certain punch press requires 2 hours longer to stamp a box of parts than does a newer-model punch press. After the old press has been punching a box of parts for 5 hours, it is joined by the new machine. Together, they finish the box of parts in 3 additional hours. How long does it take each machine, working alone, to punch a box of parts.
Thank you
Found 2 solutions by josgarithmetic, Boreal:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
                     RATES
certain old         1%2F%28x%2B2%29
new model           1%2Fx
both combined       1%2Fx%2B1%2F%28x%2B2%29

One job is "stamp a box of parts".

%281%2F%28x%2B2%29%295%2B%281%2Fx%2B1%2F%28x%2B2%29%293=1----------Most important is that this make sense and you learn to formulate it yourself.

The rest is arithmetic. Tell if you need more help.

Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
new model takes x hours to do the whole thing. In 1 hour, it does 1/x
old model takes x+2 hours to do the whole thing. In 1 hour, it does 1/(x+2)
8/(x+2)+3/x=1
x(x+2)=8x+3(x+2), clearing fractions by multiplying everything by x(x+2)
x^2+2x=11x+6
x^2-9x-6=0
x=(1/2)(9+sqrt(81+24); sqrt 105=10.25
x=(1/2)19.25=9.63 hours, only positive root. That is new punch press. The old one takes 11.63 hours.
After 5 hours,
old punch pass has done 8/11.63=0.688 of the job
the new one does 3/9.63 = 0.311 of the job