Question 223636
An experienced clerk can fill a certain order in 7 hours. A new clerk needs 10 hours to do the same job. working together, How long will it take them to fill the order. 
My answer is 8.5 hours. I added both their times together and divided by 2. 
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Since one of them can do the job in 7 hrs, it shouldn't take them
more time to do the job together. Right!
It doesn't work to add the times.  You need to work with the rates.
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Old-clerk DATA:
time = 7 hr/job ; rate = 1/7 job/hr
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New-clerk DATA:
time = 10 hr/job ; rate = 1/10 job/hr
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Together DATA:
time = x hr/job ; rate = 1/x job/hr
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Equation:
rate + rate = together rate
1/7 + 1/10 = 1/x
Multiply thru 70x
10x + 7x = 70
17x = 70
x = 70/17 hrs.
x = 4.12 hrs (time for them to do the job together)
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Cheers,
Stan H.