The Answer: painting rate problem

So this is a super simple rate problem. You just need to write down what you know and it gives you multiple equations and unknowns to solve. I think a few of these might be useful in teaching units. Possibly adding a unit conversion step in setting up the problem.

So we know that we have two rates for painting a house of area A:

	20R = A
	30r = A
      

So we can solve for values of (r,R).

	R = A/20
	r = A/30
      

      xr+xR=A
      x(A/20) + x(A/30) = A
      x(50/600) = 1
      x(1/12) = 1
      x=12
      

So we see the house takes 12 days to paint.