SOLUTION: six painters can paint 10 homes in 9 weeks. because of time constraints, the homes need to be finished in 2 weeks. how many ADDITIONAL painters must be hired to finish painting th

Question 71159: six painters can paint 10 homes in 9 weeks. because of time constraints, the homes need to be finished in 2 weeks. how many ADDITIONAL painters must be hired to finish painting the 10 homes in only two weeks?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=number of ADDITIONAL painters needed to finish painting the 10 homes in 2 weeks
Now we know that:
If six painters can paint 10 homes in 9 weeks, then
six painters can paint 10/9 homes per week and, in two weeks, six painters can paint 20/9 homes leaving only (90/9-20/9=70/9) homes to paint by the ADDITIONAL painters.
Also, one painter can paint (10/9)(1/6) or 10/54 homes per week and in two weeks, one painter can paint 20/54 or 10/27 homes. So our equation to solve is
(10/27)(x)=70/9 multiply both sides by the LCM (27)
10x=210 divide both sides by 10
x=21---------------ADDITIONAL painters needed to finish the job in 2 weeks
Another way to look at this problem:
If six painters can paint 10 homes in 9 weeks, then one painter can paint 10 homes in (6)(9) or 54 weeks and x painters can paint 10 homes in 54/x weeks.
So our equation to solve is:
54/x=2 multiply both sides by x
54=2x divide both sides by 2
x=27---------------------total required to finish in 2 weeks
27-6=21--------------------ADDITIONAL painters required

Hope this helps----ptaylor

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