Deirdre allocated a certain number of workers to do a construction job on time. She was later informed, however, that the job had to be completed in 1/4 less time and required 1/5 more work than was originally specified. She thus allocated 60 extra workers to ensure that the job would be completed on time. Assuming that all of her workers are equally productive and the speed at which each one works is constant, how many workers did she ultimately allocate to the job?
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This one took me way too long. The tricky part is realizing you don't even need to solve for the original number of workers — you can just set up the ratio between the two scenarios and let the original cancel out.
Wait, how does it cancel? I keep getting stuck with two unknowns.
Yeah once you see it as (work)/(time) = constant * workers it gets way cleaner.
The "1/4 less time" wording messed me up. I read it as time became 1/4 of the original instead of 3/4 of the original. Cost me a whole minute.
Same here, classic trap wording. Gotta read these super carefully at this level.
Got 180 by setting up W/(0.75T) needs to equal (1.2W)/T scaled by workers. Hard but satisfying once it clicks.
Nice, the 1.2W over 0.75T ratio is exactly the shortcut.
This is a 705+ for sure. The arithmetic itself isn't bad, it's just translating the two changes into the right relationship. Anyone have a clean way to avoid getting lost in the fractions?
I just plug in smart numbers for W and T to make the math less ugly.
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.