Question 1129747
The O'Connors own a small janitorial service.
 John requires 1/4 hour more time to clean the Moose club by himself than Chris does working by herself.
 If together they can clean the club in 4 ​hours, find the time required by each to clean the club.
:
let t = time required by Chris working alone
then
(t+.25) = time required by John
the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1
{{{4/t}}} + {{{4/((t+.25))}}} = 1
multiply equation by t(t+.25), cancel the denominators
4(t+.25) + 4t = t(t+.25)
4t + 1 + 4t = t^2 + .25t
8t + 1 = t^2 + .25t
arrange as a quadratic equation on the right
0 = t^2 +.25t - 8t - 1
t^2 - 7.75t - 1 = 0
use the quadratic formula: a=1; b=-7.75; c=-1
I got a positive solution of
t = 7.877 hrs Chris alone
and
7.877 + .25 = 8.127 hrs John alone