4 men and 3 women finish a job in 6 days, and 5 men and 7 women can do the same job in 4 days. How long will 1 man and 1 woman take to do the work?

Answer 1

Assumption must be made that all men are equally efficient and all women are equally efficient.

m represents the work of 1 man

w represents the work of 1 woman

J represents the entire job

4m + 3w = J/6 one days work

5m + 7w = J/4 one days work

8m + 6w = 2J/6 multiply top equation by 2

13m + 13w = 2J/6 + P/4 add two equation

13m + 13w = 4J/12 + 3P/12

13m + 13w = 7J/12

m + w = 7J/(12*13)

m + w = 7J/156

The two take 156/7 or 22 and 2/7 days