A chef can bake a certain number of cakes in a given amount of time. An assistant can bake thrice as many pies in twice the time. It takes twice as long to bake a cake than it does a pie. If, together, they can bake 20 cakes and 30 pies in 4 hours, how many pies can the chef alone bake in an hour?
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This one took me way longer than it should have. The "twice as long to bake a cake" conversion is where I kept tripping up.
Same. I set it up as c = 2p and then everything fell into place, but the first two minutes were rough.
Honestly the wording makes it feel harder than the math actually is.
Can someone explain why we have to convert cakes to pie-equivalents? I tried keeping them separate and got a nonsense equation.
Because the times are linked. If a cake takes twice as long as a pie, one cake = 2 pie-units of work time. Then you can add everything in the same unit.
Solid 700+ question. The trap answer is definitely in there for people who forget the chef bakes cakes but the question asks for pies.
Yep, I initially solved for the chef's cake rate and almost picked it. Reread the last line just in time.
Got there by letting the pie rate be p per hour. Chef's cake rate is p/2, assistant pies = 3p/2. Then 4h of combined work gives the total. Clean once you see it.
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.