SOLUTION: A alone would take 6 hours more to complete the job than if both A and B would work together. When B worked alone he took 1.5 hours more to complete the job and A and B worked toge

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A alone would take 6 hours more to complete the job than if both A and B would work together. When B worked alone he took 1.5 hours more to complete the job and A and B worked toge      Log On


   

Question 924413: A alone would take 6 hours more to complete the job than if both A and B would work together. When B worked alone he took 1.5 hours more to complete the job and A and B worked together. How much time they will take if they work together?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A alone would take 6 hours more to complete the job than if both A and B would work together.
When B worked alone he took 1.5 hours more to complete the job and A and B worked together.
How much time they will take if they work together?
:
let t = time required when A & B work together
Let the completed job = 1
t%2Fa + t%2Fb = 1
:
" A alone would take 6 hours more to complete the job than if both A and B would work together.
%28%28t%2B6%29%29%2Fa = 1
therefore
a = t+6
" When B worked alone he took 1.5 hours more to complete the job and A and B worked together."
%28%28t%2B1.5%29%29%2Fb = 1
therefore
b = t+1.5
Replace a & b in the 1st equation
t%2F%28%28t%2B6%29%29 + t%2F%28%28t%2B1.5%29%29 = 1
multiply the equation by (t+6)(t+1.5), cancel the denominators, we have:
t(t+1.5) + t(t+6) = (t+6)(t+1.5)
t^2 + 1.5t + t^2 + 6t = t^2 + 1.5t + 6t + 9
2t^2 + 7.5t = t^2 + 7.5t = 9
2t^2 - t^2 + 7.5t - 7.5t = 9
t^2 = 9
t = 3 hrs if they work together?
:
:
We can check this, now we know that a would take 9 hrs alone and b take 4.5 hr
3%2F9 + 3%2F4.5 = 1
.333 + .667 = 1