SOLUTION: Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only t      Log On


   

Question 524142: Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only takes five hours to paint the whole house. How long would it take Joe to paint the house if he worked alone?
Found 3 solutions by mananth, stanbon, Edwin McCravy:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Painting the house 1 job
Kevin 12 hours
He does 1/15 job in 1 hour
Nick 15 hours
He does 1/30 of thejob in 1 hour
Joe x hours
It does 1/x of the job in 1 hour
They all take 5 hours
so they do 1/5 of job in 1 hour

Together they will do 1/15 + 1/12 + 1/x= 1/5
1/15 + 1/12 - 1/5=-1/x
LCD = 60
(4+5-12)/60 =-1/x
-3/60=-1/x
-1/20=-1/x
x= 20 hours.
Joe takes 20 hours alone

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only takes five hours to paint the whole house. How long would it take Joe to paint the house if he worked alone?
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kevin rate = 1/12 job/hr
---
Nick rate = 1/15 job/hr
----
Joe rate = 1/x job/hr
----
Together rate = 1/5 job/hr
-----
Equation:
rate + rate + rate = together rate
1/12 + 1/15 + 1/x = 1/5
----
Multiply thru by 60x to get:
5x + 4x + 60 = 12x
3x = 60
x = 20 (time for Joe to do the job alone)
----
Cheers,
Stan H.
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Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Three brothers decide to paint their house. Kevin could paint the house in 12 hours, and Nick could paint it in 15 hours. When they work together with their brother, Joe, it only takes five hours to paint the whole house. How long would it take Joe to paint the house if he worked alone?
Make this chart:

                   Number of        Hours          Rate in
                Houses Painted     Required      Houses/Hour
Kevin alone

Nick alone

Joe alone

All together


Let x be the hours required for Joe to paint it alone.  Fill in the other
times which are given.  Also fill in 1 for the number of houses painted in
each case because in all 4 situations 1 house is painted.

                   Number of        Hours          Rate in
                Houses Painted     Required      Houses/Hour
Kevin alone           1              12

Nick alone            1              15

Joe alone             1               x

All together          1               5

Next fill in the rates in Houses/Hour by dividing the number of
houses painted by the hours:

                   Number of        Hours          Rate in
                Houses Painted     Required      Houses/Hour
Kevin alone           1              12             1%2F12
Nick alone            1              15             1%2F15
Joe alone             1               x             1%2Fx   
All together          1               5             1%2F5

The equation comes from:

Kevin's rate + Nick's rate + Joe's rate = their rate all together

                   1%2F12 + 1%2F15 + 1%2Fx = 1%2F5

Multiply through by LCD of 60x and solve for x.

Answer:  x = 20 or it would take Joe 20 hours to paint the house alone.

Edwin