Machine A can complete a job in 12 hours, and Machine B can do the same job at 1/5 of the rate of Machine A. If Machine A completes 3/4 of the job and then Machine B finishes the remaining portion, what is the total amount of time taken by Machine A and Machine B?
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Got this one pretty quick once I realized B's rate is 1/5 of A's. Nice medium-easy rate problem.
same, the 1/5 wording threw me for like 20 seconds though lol
Yeah once you convert B's rate it's smooth sailing.
Can someone explain why we don't just average the two rates? I keep wanting to do that out of habit.
Because they're not working at the same time — A does part, then B does the rest. Averaging is for simultaneous work.
The 3/4 detail is what makes this one interesting. Remaining 1/4 at a slower rate takes longer than people expect.
right? I initially assumed B was fast and almost picked 24
Wait, is B's rate 1/5 of A meaning B takes 5x as long? Just want to confirm I set it up right.
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.