SOLUTION: Phil can paint the garage in 12 hours and Rick can do it in 10 hours. They work together for 3 hours. How long will it take Rick to finish the job alone? Notice: Although they work

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Phil can paint the garage in 12 hours and Rick can do it in 10 hours. They work together for 3 hours. How long will it take Rick to finish the job alone? Notice: Although they work      Log On


   

Question 132056: Phil can paint the garage in 12 hours and Rick can do it in 10 hours. They work together for 3 hours. How long will it take Rick to finish the job alone? Notice: Although they work for 3 hours, they did not finish the job. Please help me and answer this. If you could explain fully, clearly, and easily, that would be wonderful. Thanks!
Found 2 solutions by edjones, bucky:
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Phil can do the 1/12 job in 1 hr.
Rick can do 1/10 job in 1 hr.
In 3 hours: 3/12 + 3/10
=15/60 + 18/60
=33/60=11/20 of the job is completed after 3 hrs.
.
Rick has to finish 9/20 of the job.
Let x be the number of hours required for Rick to complete the job.
x/10=9/20
x=90/20
x=4.5 hrs it will take Rick to finish the job alone.
.
Ed

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Phil can paint the garage in 12 hours. That means that each hour he does 1/12 of the job.
.
Rick can paint the garage in 10 hours. That means that each hour he does 1/10 of the garage.
.
If they work together for 3 hours, Phil does 3 times 1/12 of the garage so he does 3/12 or 1/4 of
the garage or in decimals 0.25 of the garage.
.
At the same time Rick who does 1/10 of the garage every hour does 3/10 of the garage in the
3 hours and in decimals this is 0.30 of the garage.
.
So in three hours of working together, their combine progress is 0.25 + 0.30 = 0.55
.
This means that of the entire garage they have done 0.55 of it. So there is 0.45 of it left
(1 - 0.55 = 0.45).
.
At this point Phil quits and Rick presses on by himself. Since he does 1/10 of the garage every
hour and there are 4.5 tenths of the garage left, it will take Rick 4.5 hours more to
complete the garage.
.
You can get that from the equation:
.
1/10 * T = 0.45
.
where T represents the time that Rick needs to complete the job after Phil goes on strike.
.
Multiply both sides of this equation by 10 and it becomes:
.
T = 4.5 hours
.
Hope this helps you to understand the problem and enables you to see your way through it in
a logical fashion. The whole trick to this method begins by recognizing that if a person can
do the entire thing by him/herself in x hours, then each hour (s)he does 1/x of the job.
.