nkmungila wrote:

10 men take 30 minutes to wrap 100 articles. How long will it take 40 men to wrap 200 articles if the new team is half as efficient?

A. 7.5 minutes

B. 15 minutes

C. 30 minutes

D. 60 minutes

E. 120 minutes

Attachment:

WRTvar.png [ 24.34 KiB | Viewed 858 times ]
One quick way (well under a minute): Modify the standard R*T= W formula. Add

Number of workers (or machines, etc.) to LHS

Modified RTW formula: (

# of workers) * R * T = WUse the first scenario to find unknowns in second scenario.

Here, find Group 1's individual rate to find rate and time for Group 2.

1) Individual worker rate for Group 1?

W = (# of workers) * R * T\(100 = 10 * R * 30\)\(\frac{100}{(10 * 30)} = R\)

\(R = \frac{100}{300}\) =

\(\frac{1}{3}\)2) Group 2 individual rate?

Individual worker rate in Group 1 = \(\frac{1}{3}\)

Group 2 workers are half as efficient:

\(\frac{(\frac{1}{3})}{2} = (\frac{1}{3} * \frac{1}{2} ) =\) \(\frac{1}{6}\)= individ rate of Group 2

3) How long will it take 40 men [working at Group 2's individual rate] to wrap 200 articles?

W = (# of workers) * R * TIME\(200 = 40 * \frac{1}{6}* TIME\)

\(TIME = \frac{200}{(40 * \frac{1}{6})} = \frac{200}{(\frac{40}{6})}\)

\(TIME = 200 * (\frac{6}{40}) = (5 *6) =\)30 minutesAnswer C

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