SOLUTION: A piece of manufacturing equipment can produce enough items to fill an order in 10 hours. If an auxiliary piece of equipment is used also, it will take 7 hours. How long would it t
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Question 1095086: A piece of manufacturing equipment can produce enough items to fill an order in 10 hours. If an auxiliary piece of equipment is used also, it will take 7 hours. How long would it take the auxiliary equipment to fill the order working alone? Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52787) (Show Source):
The combined rate of work is of the job per hour.
The known individual rate of work is .
It implies that the unknown individual rate of work is = = .
Hence, it will take = 23 hours and 20 minutes for the auxiliary equipment to fill the order working alone.
You can put this solution on YOUR website! The solution supplied by ikleyn is a perfectly good traditional algebraic one. I find many students prefer a different method. Here it is for your problem; give it a try and see if maybe it "works" better for you than the traditional algebraic method.
(1) Take the 10 hours that the one piece of equipment takes to do the job, and the 7 hours that it takes the two pieces together to do the same job.
(2) Consider a period of 70 hours, where 70 is the least common multiple of 10 and 7. In those 70 hours, the first piece of equipment could do this job 70/10 = 7 times; together the two pieces of equipment could do the job 70/7 = 10 times. That means the second piece of equipment could do the job 3 times in those 70 hours. Doing the job 3 times in 70 hours means doing the job once in 70/3 hours.
