Four boys and ten girls can cut a field first 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?
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Correct Answer: Option D
Explanation:
Let x rep. numbers of boys that can work at \(\frac{5}{4}\) the rate at
which the 10 girls work
or 1 hrs, x boys will work for \(\frac{\frac{1}{5} \times 10}{4}\)
x = \(\frac{5}{4}\) x 10
= 8 boys
8 boys will do the work of ten girls at the same rate
4 + 8 = 12 bous cut the field in 5 hrs for 3 hrs,
\(\frac{12 \times 5}{3}\) boys will be needed = 20 boys.
Let x rep. numbers of boys that can work at \(\frac{5}{4}\) the rate at
which the 10 girls work
or 1 hrs, x boys will work for \(\frac{\frac{1}{5} \times 10}{4}\)
x = \(\frac{5}{4}\) x 10
= 8 boys
8 boys will do the work of ten girls at the same rate
4 + 8 = 12 bous cut the field in 5 hrs for 3 hrs,
\(\frac{12 \times 5}{3}\) boys will be needed = 20 boys.