Working together at their respective constant rates, robot A and robot B polish 88 pounds of gemstones in 6 minutes. If robot A’s rate of polishing is 3/5 that of robot B, how many minutes would it take robot A alone to polish 165 pounds of gemstones?
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Got it in about 1:45. The 3/5 ratio is the key — just set B's rate as 5x and A's as 3x, then use the combined 88 lbs in 6 min. Once you get A's rate, 165 lbs is straightforward.
Yeah, same approach. The ratio setup makes it clean, no messy fractions.
Took me a while because I kept trying to set up A + B = 88/6 directly with fractions. Setting B = 5x and A = 3x was way cleaner. Solid 605-655 level trap.
Classic ratio-vs-actual-rate confusion. I did the same thing first pass.
Same here, the 3/5 wording tripped me up initially.
Wait, when I got A's rate I had 44/3 lbs per minute... is that right?
That's what I got too. Then it's just 165 divided by that.
Nice question. Not too hard but the ratio setup can waste time if you're not careful. Under 2 minutes if you spot the substitution quickly.
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.