Machine A takes 2 more hours than machine B to make 20 widgets. If working together, the machines can make 25 widgets in 3 hours, how long will it take machine A to make 40 widgets?
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This one had me stuck for a while. I set B's time to make 20 widgets as t, so A takes t+2. Then together rate is 20/t + 20/(t+2) = 25/3. Solving that quadratic was a bit messy but doable. Is there a faster way to backsolve? The answer choices are all integers, so maybe plugging in could work.
Backsolving is definitely faster here. Just test the options: if A takes x hours for 40 widgets, then for 20 widgets it's x/2. So B takes x/2 - 2 hours. Then check if combined rate makes 25 in 3 hours. Only one works.
I tried backsolving but got mixed up with the 20 vs 40 widgets. Need to be careful with the conversion.
The algebra isn't too bad if you simplify early. Let A's time for 20 widgets be a, B's be b. We have a = b+2 and 1/a+1/b = 25/60 = 5/12. Substitute and solve. I got a nice integer, so it works out.
Wait, the question asks for A to make 40 widgets, not 20. So once you find A's time for 20, you just double it. I almost missed that.
Yeah, that's the trick. The answer choices are all even, so doubling is easy.
This is a classic work-rate problem but the twist with 20 vs 25 widgets and then asking for 40 makes it tricky. I had to read it twice.
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.