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?
:
let t = time required when A & B work together
Let the completed job = 1
{{{t/a}}} + {{{t/b}}} = 1
:
" A alone would take 6 hours more to complete the job than if both A and B would work together.
{{{((t+6))/a}}} = 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."
{{{((t+1.5))/b}}} = 1
therefore
b = t+1.5
Replace a & b in the 1st equation
{{{t/((t+6))}}} + {{{t/((t+1.5))}}} = 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
{{{3/9}}} + {{{3/4.5}}} = 1
.333 + .667 = 1