20 archivists, each working at the same constant rate, can catalog a collection in 15 hours. After how many hours from the start should 8 archivists be reassigned and stop working so that the remaining archivists finish cataloging the entire collection in 10 hours after the reassignment?
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Wait, I'm getting confused by the wording. Does "finish in 10 hours after the reassignment" mean the total time is 10 hours from the start, or 10 more hours after those 8 people leave? I keep getting two different numbers and neither is in the choices, so I must be misreading it.
Same here. I think it means 10 hours AFTER the reassignment, so total time = x + 10. That interpretation gave me an answer that's actually on the list lol.
Let me set it up as total work = 20 archivists × 15 hours = 300 archivist-hours. Before the switch, all 20 work for x hours, then only 12 work for the remaining 10 hours. So 20x + 12(10) = 300. That should nail it.
This is the cleanest way to think about it. The ones who leave don't contribute anything after hour x, so you just account for their work up front.
Yes, this is the standard "combined rate then partial" setup. Just be careful — 12, not 8, when you compute the remaining workforce.
Classic trap answer is probably one of the choices you get if you use 8 instead of 12 for the second phase. I almost fell for it until I re-read "remaining archivists."
Yep, they always plant the distractor that matches the wrong number. I've learned to double-check who's actually still working.
Honestly this one felt more like a 600-level question. Once you get that total work stays constant, it's just x + (12/20)(10) = 15, which isn't too bad. The wording is the only tricky part.
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.