SOLUTION: A Painter can do a given job in 6hours. Her helper can do the same job in 10 hours. The painter begins the work and after two hours is joined by the helper. In how many hours will

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A Painter can do a given job in 6hours. Her helper can do the same job in 10 hours. The painter begins the work and after two hours is joined by the helper. In how many hours will       Log On


   

Question 551352: A Painter can do a given job in 6hours. Her helper can do the same job in 10 hours. The painter begins the work and after two hours is joined by the helper. In how many hours will the complete the job? Please, thank you~ Happy New Year to you, Great Tutors! <3
Found 2 solutions by nerdybill, mananth:
Answer by nerdybill(7384) About Me  (Show Source):
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A Painter can do a given job in 6hours. Her helper can do the same job in 10 hours. The painter begins the work and after two hours is joined by the helper. In how many hours will the complete the job?
.
Let x = time (hours) worked by Painter (also to complete job)
then
x-2 = hours worked by helper
.
x(1/6) + (x-2)(1/10) = 1
multiplying both sides by 60:
x(10) + (x-2)(6) = 60
10x + 6x-12 = 60
16x - 12 = 60
16x = 72
x = 72/16
x = 4.5 hours

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Painter can do the job in 6hours
he does 1/6 of the job in 1 hour
he works for 2 hours
so he completes 2/6 of the job = 1/3
balance job = 1-1/3 = 2/3
Helper does the job in 10 hours
so he does 1/10 of the job in 1 hour.
Together they can do 1/6 + 1/10 of the job in 1 hour
=8/30 ==> 4/15 of the job in 1 hour
4/15 of the job they do in 1 hour
2/3 of the job they will do in (2/3) /(4/15)
=2/3 * 15/4
=30/12
=2.5 hours
Balance job they complete in 2 1/2 hours
Happy New Year