Three printing presses, R, S, and T, working together at their respective constant rates, can do a certain printing job in $4$ hours. S and T, working together at their respective constant rates, can do the same job in $5$ hours. How many hours would it take R, working alone at its constant rate, to do the same job?

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Comments

BebasApr 23

Wait, is it really this simple? Combined rate = 1/4, S+T = 1/5, so R = 1/4 - 1/5 = 1/20. That gives 20. Am I missing something?

SusieApr 26

Nope, that's exactly it. These sub-505 rate problems are basically just subtraction of fractions.

AdityaApr 26

I did the same thing but second-guessed myself because it felt too easy lol

AamirkMay 3

Got E. 20 hours. Nice confidence boost after the last few rate problems I tanked.

DhevaMay 4

Same here, these "work together" ones always trip me up when there are 3 machines, but this one was clean.

MariaAug 24

Quick tip that helped me: always convert to "jobs per hour" first, never leave it in hours per job. 1/4 - 1/5 is way easier to see than trying to reason about it directly.

RishikSep 6

This is the move. I used to try to set up an RT=W equation and overthink it.

RachelJun 9

Why is R's time bigger than the combined time of all three? That part confused me for a sec until I realized R is slower than S and T together.

JanetJun 23

Yeah, since S and T alone take 5 hrs, R has to be slower than them combined, so answer must be more than 5 but the math pins it down. Good sanity check though.

What this question tests

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.