Machine M operates at a consistent rate and completes a task in three times the time it takes for machine N to finish the same task. When machine M and machine N work together at their respective constant rates, they can complete the job in hours. How many hours does it take for machine N to complete the job on its own?
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Thanks, this one finally clicked for me. I set N's time as t and M's as 3t, then used the combined rate equation. Easy but I always mess up the reciprocal part.
Same here. The trick is remembering rate = 1/time, not just time itself.
Yeah once you write 1/t + 1/(3t) = 1/6 it's basically over.
Why do we let N be t and not M? I did it the other way and got confused with the 3t.
It works either way, just pick the variable for the one you're solving for to avoid extra algebra.
Got C. Pretty straightforward for a sub-500 question. The combined work formula did all the heavy lifting.
Quick question: does the 3 times mean M takes longer, so M is the slower machine? I almost flipped it.
Yes, slower machine = longer time = smaller rate. Keep that straight and you're fine.
What it tests
Your ability to combine individual work rates, usually by working with the fraction of a job completed per unit of time.
Common trap
Adding the times instead of the rates, or forgetting to take the reciprocal when combining rates.