SOLUTION: Company #1 makes 1 case every 2 seconds. Company #2 make 1 case every 3 seconds. How many seconds does it take to make 10 cases if the companies work together. What is the equation

Question 522887: Company #1 makes 1 case every 2 seconds. Company #2 make 1 case every 3 seconds. How many seconds does it take to make 10 cases if the companies work together. What is the equation?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Since company #1 makes a case every 2 seconds, its rate of production is 1/2 case per second.
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Since company #2 makes a case every 3 seconds, its rate of production is 1/3 case per second.
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So the rate of production for the two companies working together is 1/2 plus 1/3 case per second. Since 1/2 is equal to 3/6 and 1/3 is equal to 2/6, the combined rate is (by adding) 5/6 case per second.
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The time that it takes to produce 10 cases can now be determined by dividing the 10 cases by the rate of 5/6 case per second. To divide by a fraction (5/6 in this case) you invert the fraction and multiply. In other words, the time is determined by multiplying the 10 cases times the inverted fraction 6/5.
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The result of this multiplication of 10*6/5 = 60/5 = 12. So when the two companies work together, they will produce 10 cases in 12 seconds. 12 seconds is the answer to this problem. (Note that in 12 seconds company #1, operating at the rate of 1 case every 2 seconds will make 6 cases. Similarly company #2, operating at the rate of 1 case every 3 seconds will make 4 cases in 12 seconds. Therefore, the two companies produce a total of 10 cases in the 12 seconds.)
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Hope this helps you to understand the problem. The most difficult thing to see in the process to find the answer is that you have to determine the rate in a common unit of time. In this problem, we used a second for the time unit and then determined how much of a case could be produced by each company in that unit of time. Then we added the two rates together to see how many cases could be produced each second when the two companies were working together.
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