Question 1176203
 An old printing press takes 5 hours longer to put out a daily paper than does a new press.
 If the two press work together, the job takes 6 hours.
 How long does it take each press to put out the paper on its own?
:
let t = time required by the new press to do the job
then
(t+5) = time required by the old press
let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1
{{{6/t}}} + {{{6/((t+5))}}} = 1
Multiply by t(t+5), cancel the denominators
6(t+5) + 6t = t(t+5)
6t + 30 + 6t = t^2 + 5t
12t + 30 = t^2 + 5t
form a quadratic on the right'
0 = t^2 + 5t - 12t - 30
t^2 - 7t - 30 = 0
Factors to
(t-10)(t+3) = 0
positive solution is all we want here
t = 10 hrs required by the new press
then, obviously
15 hrs required by to old press
:
:
See if that works
{{{6/10}}} + {{{6/15}}} = 
{{{3/5}}} + {{{2/5}}} = 1