2 men and 7 boys can do a piece of work in 4 days.The same work is done in 3 days by 4 men and 4 boys.How long would it take for one man and one boy to do it?
2 men and 3 boys can do a piece of work in 16 days.
5 men and 6 boys can do a piece of work in 7 days.
4 men and 8 boys can do a piece of work in ? days.
D = RT
Let a combination of m + b be the "rate" in this problem.
(2m + 3b)16 = (5m + 6b)7
32m + 48b = 35m + 42b
-3m = -6b
m = 2b
1m = 2b.
We now know 1 man equals workload of 2 boys.
Basically now (since 1 men = 2boys)
5 boys can do the work in 16 days.
16 boys can do the work in 7 days.
16 boys can do the work in 7 days.
But 16 boys is the equivalent of 4 men and 8 boys, so it's 7 days.