Alex can do three times as much work per hour as Bruno. As a result, Alex takes 12 hours fewer than Bruno to complete a certain job. In how many hours can Bruno complete the job working alone?
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Got this one right — the key is that Alex does 3x work per hour, so if Bruno takes b hours, Alex takes b/3. The difference is 12, so b - b/3 = 12. Nice and clean once you set it up that way.
This is the setup I needed, was overcomplicating it with a combined job value. Thanks!
Why is everyone setting b - b/3 = 12? I tried to do 3x - x = 12 at first and got confused. Can someone explain the variable choice?
You want both times in terms of the same person. If Bruno's time is b, Alex's time is b/3, so the difference in times is b - b/3.
Solid 500-level work/rate question. Not too bad if you've drilled the time-is-inverse-of-rate idea. Took me about 90 seconds.
I plugged choices in. Tried 18 for Bruno, so Alex would take 6, difference is 12. Works. Fastest way if you blank on the algebra.
Backsolving is underrated on rate problems. Going to start doing that when the algebra setup isn't obvious.
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.