Two women,Sita and Gita,working separately ca | vedclass

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(A) Sita's work rate is $\frac{1}{8}$ field/hr and Gita's work rate is $\frac{1}{12}$ field/hr.In the first $2 \, hrs$ (one hour each),the work done i

Vedclass · Accepted Answer

$6:30$

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(A) Sita's work rate is $\frac{1}{8}$ field/hr and Gita's work rate is $\frac{1}{12}$ field/hr.In the first $2 \, hrs$ (one hour each),the work done is $\frac{1}{8} + \frac{1}{12} = \frac{3+2}{24} = \frac{5}{24}$ of the field.In $8 \, hrs$ ($4$ cycles of $2 \, hrs$),the work done is $\frac{5}{24} 	imes 4 = \frac{5}{6}$ of the field.Remaining work $= 1 - \frac{5}{6} = \frac{1}{6}$.In the $9^{th} \, hr$,Sita works and completes $\frac{1}{8}$ of the field.Remaining work after $9 \, hrs = \frac{1}{6} - \frac{1}{8} = \frac{4-3}{24} = \frac{1}{24}$.In the $10^{th} \, hr$,Gita works. She completes $\frac{1}{12}$ of the field in $1 \, hr$,so she will complete $\frac{1}{24}$ of the field in $\frac{1}{24} \div \frac{1}{12} = 0.5 \, hr$.Total time $= 9.5 \, hrs$.Starting at $9:00 \, a.m.$,$9.5 \, hrs$ later is $6:30 \, p.m.$

Two women,Sita and Gita,working separately can mow a field in $8$ and $12 \, hrs$ respectively. If they work in stretches of one hour alternatively,with Sita beginning at $9:00 \, a.m.$,when will the mowing be finished? (in $p.m.$)

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