Rachel T.

asked • 11/20/14

One grocery clerk can stock a shelf in 45 min.

A second clerk requires 40 min to stock the same shelf. How long would it take to stock the shelf if the two clerks worked together?

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Christopher R. answered • 11/20/14

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Rachel, this is simply a work problem.
 
Let t= the time it takes for both grocery clerks to stock a shelf together.
 
1/40+1/45=1/t Multiply the equation by (40)(45)t to simplify the arithmetic.
 
45t+40t=(40)(45)=1800
 
95t=1800  Divide both sides of the equation by 95.
 
t≅19.95 Hence, it would take about 19.95 minutes for both grocery clerks to stock a shelf working together. 
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Bill P.

There is a mistake in the above solution. 45t + 40 t = 85t, not 95t.
 
Thus t = 1800/85 or about 21.18 minutes.
 
Note: I knew there was a mistake when a saw the answer was less than 20 minutes. It would take exactly 20 minutes to complete this task if each clerk could complete this task in 40 minutes alone. Since the one clerk is a bit slower, it must take more than 20 minutes (but also less than 22.5 minutes (half of 45 minutes) ) 
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04/05/15

Christopher R.

I'm bad. I just made a simple arithmetic error. 40 +45=85, not 95. Hence, 85t=1800 in which t=21.18 minutes. 
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04/05/15

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