Question 507565: In 2 mins. a conveyor belt moves 300 lbs of aluminum from the delivery truck to a storage area. A smaller belt moves the same quantity of cans the same distance in 6 mins. If both belts are used, find how long it takes to move the cans to storage.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! In doing problems like this, you need to consider each thing as doing a faction of the whole job.
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The larger conveyor does the work in 2 minutes, so it does 1/2 the job per minute.
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The smaller conveyor does the work in 6 minutes, so it does 1/6 of the job per minute.
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x = unknown number of minutes working together
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(1/2 + 1/6) x = 1 whole job
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(6/12 + 2/12)x = 1
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(8/12)x = 1
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x = 12/8 = 3/2
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x = 1 1/2 minutes
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Always check your work.
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Working for 1 1/2 minutes, the larger conveyor does 3/2*1/2 = 3/4 of the job (recalling it can do the whole job in 2 minutes).
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Working for 1 1/2 minutes the smaller conveyor can do 3/2 * 1/6 = 3/12 = 1/4 of the job.
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Correct.
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Answer: Working together it will take 1 1/2 minutes or 1 min 30 sec.
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Done
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