Four boys and ten girls can cut a field in 5 hours if the boys work at 54 5 4 the rate at which the girls work. How many boys will be needed to cut the fiel...

Four boys and ten girls can cut a field in 5 hours if the boys work at $\frac{5}{4}$ the rate at which the girls work. How many boys will be needed to cut the field in 3 hours?

Answer Details

Let x represents number of boys that can work at $\frac{5}{4}$ the rate at which the 10 girls work
For 1hr. x boys will work for $\frac{\frac{1}{5}}{4}$ x 10
x = $\frac{4}{5}$ x 10 = 8 boys
8 boys will do the work of ten girls at the same rate 4 + 8 = 12 boys cut the field in 5 hrs
For 3 hrs, $\frac{12\times 5}{3}$ boys will be needed = 20 boys