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Jenny takes 3 hours to sand a picnic table; Laila can do the same job in \(\dfrac{1}{2}\) hour...

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Jenny takes 3 hours to sand a picnic table; Laila can do the same job in \(\dfrac{1}{2}\) hour...

by BTGmoderatorLU » Thu Aug 20, 2020 4:51 am

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Jenny takes 3 hours to sand a picnic table; Laila can do the same job in \(\dfrac{1}{2}\) hour. Working together at their respective constant rates, Jenny and Laila can sand a picnic table in how many hours?

A. \(\dfrac{1}{6}\)
B. \(\dfrac{2}{9}\)
C. \(\dfrac{1}{3}\)
D. \(\dfrac{3}{7}\)
E. \(\dfrac{5}{6}\)

The OA is D
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Re: Jenny takes 3 hours to sand a picnic table; Laila can do the same job in \(\dfrac{1}{2}\) hour...

by deloitte247 » Sat Aug 22, 2020 1:05 pm
$$Rate\ =\ work\ done\ per\ unit\ of\ time$$
$$Rate\ =\ \frac{workdone}{time}$$
$$Jenny's\ rate\ =\ 1\ table\ in\ 3\ hours=\frac{1}{3\ }table\ per\ hour$$
$$Laila's\ rate\ =\ 1\ table\ in\ \frac{1}{2}hours=1\div\frac{1}{2\ }=\ 1\cdot\frac{2}{1}$$
$$=\ 2\ tables\ per\ hour$$
$$Working\ together\ =>$$
$$Total\ rate\ =>\ \frac{total\ work\ done}{time}$$
$$\frac{Combined}{total\ rate}\ =\ \frac{1}{3}+\frac{2}{1}=\frac{1+6}{3}=\frac{7}{3}$$
$$Two\ of\ them\ can\ sand\ \frac{7}{3\ }picnic\ table\ per\ hour$$
$$Time\ taken\ for\ the\ 2\ of\ them\ to\ sand\ 1\ picnic\ table\ $$
$$=\ time\ taken\ =\frac{total\ workdone}{total\ rate}$$
$$time\ =\ 1\div\frac{7}{3}$$
$$=\ 1\cdot\frac{3}{7}=\frac{3}{7\ }hours$$
$$Answer\ =\ D$$
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