SOLUTION: 2 men take 16 hrs to paint a house. 4 women take 16 hrs. to paint a house. If a group of 6 women, at the above women rate, and a group of 4 men, at the above men rate, work t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: 2 men take 16 hrs to paint a house. 4 women take 16 hrs. to paint a house. If a group of 6 women, at the above women rate, and a group of 4 men, at the above men rate, work t      Log On


   



Question 887493: 2 men take 16 hrs to paint a house.
4 women take 16 hrs. to paint a house.
If a group of 6 women, at the above women rate,
and a group of 4 men, at the above men rate,
work together to paint one house, how long will it take?

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The one-man rate is 1/32 house per hour;
and the one-woman rate is 1/64 house per hour.
They were picked that way using rates of agents working together being additive.

6 women and 4 men together:
4%281%2F32%29%2B6%281%2F64%29 the rate for this group, houses per hour.
4%2A2%2F64%2B6%2F64
%288%2B6%29%2F64
14%2F64
7%2F32, this group rate.

If you want how many HOURS per HOUSE, find the reciprocal.
32%2F7 hours per house. 4%264%2F7 hours.