A computer can perform 30 identical tasks in six hours. At that rate, what is the minimum number of computers that should be assigned to complete 80 tasks within three hours?
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Wait, is the answer 5? I got 5.33 so I rounded up to 6. But 5.33 means you need more than 5, so 6. But I'm not sure if I did it right.
Yeah, you have to round up because you can't have a fraction of a computer. So 6 is correct.
But 5.33 rounded up is 6, but 5.33 is less than 6, so 5 computers would be enough? No, 5 computers would only do 75 tasks in 3 hours, so you need 6.
I set it up as: 1 computer does 30 tasks in 6 hours, so rate = 5 tasks/hour. For 80 tasks in 3 hours, need 80/3 = 26.67 tasks/hour. So number of computers = 26.67/5 = 5.33, so 6 computers. Answer C.
That's exactly how I did it. But I initially got 5.33 and thought maybe I could round down, but that wouldn't finish the tasks.
This seems like a classic work-rate problem. The trap is to forget to round up to the next whole number. I almost picked 5 because 5.33 is closer to 5, but you need to complete all tasks, so 6 is the minimum.
I got 6. But I'm wondering if there's a faster way without finding the rate per computer. Like maybe set up a proportion?
You can do: (30 tasks)/(6 hours * 1 computer) = (80 tasks)/(3 hours * n computers). Cross multiply and solve for n. Same thing.
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.