Combined Rate of Nail-Producing Machines

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Machine A produces nails at a uniform rate of 120 every 10 seconds, and Machine B produces nails at a uniform rate of 100 every 15 seconds. If the two machines run simultaneously, how many seconds will it take for them to produce a total of 140 nails?

Review: Combined Rate of Nail-Producing Machines


Explanation

Since these machines work independently, their rates add:



We almost have x. Simplifying and trying to avoid substantial computation:







Cross-multiplying:





And finally, we can perform the long division:



The correct answer is (B).


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