Question 71159

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