SOLUTION: 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

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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.

Found 3 solutions by josmiceli, ankor@dixie-net.com, ikleyn:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +t+ = time in hrs required by Chris
to clean the Moose club
Add their rates of cleaning to get rate
working together
+1%2F%28%285%2F4%29%2At%29+%2B+1%2Ft+=+1%2F4+
+4%2F%285t%29+%2B+1%2Ft+=+1%2F4+
Multiply both sides by +5%2A4t+
+16+%2B+20+=+5t+
+5t+=+36+
+t+=+7.2+ hrs
and
+%285%2F4%29%2A7.2+=+9+ hrs
Chris takes 7 hrs 12 min
John takes 9 hrs
------------------------------
check:
+1%2F9+%2B+1%2F7.2+=+.25+
+.11111+%2B+.13888+=+.25+
+.25+=+.25+
OK

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Ft + 4%2F%28%28t%2B.25%29%29 = 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

Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.

@josmiceli misread the condition and actually solved ANOTHER problem.