Machine A currently takes x hours to complete a certain job. Machine B currently takes y hours to complete the same job. If x=4y, by what percent will x have to decrease so that A and B together can complete the job in 3y/8 hours?
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Whoa, this one took me way longer than it should have. The x = 4y substitution is fine, but setting up the combined rate equation with the new time tripped me up. Anyone else keep trying to solve for x directly instead of the percent decrease?
Same here. I had to re-read it twice before realizing I need to find the new x first, then compare it to the original.
The trap is definitely doing all the algebra correctly and then forgetting the final percent-decrease step. Classic.
705-805 feels right for this. Not conceptually brutal, but there are like three places to slip. Solid question.
Yeah, the fractions with 3y/8 are what got me. Rest of it is standard combined work.
Quick approach that worked for me: pick y = 8 so the target time is an integer, then let the rates do the work. Way less messy than dragging y around.
Smart. I always forget I can just pick numbers when the answer is a percent.
Can someone explain why we set the new combined rate equal to 1 divided by 3y/8? I get that rate = work/time, but I keep messing up which x is the new one.
You're solving for the new x that makes the combined rate match the target time. The original x is only there to set up the relationship with y, so be careful not to plug it back in at the end.
Think of it as: new A rate + B rate = 1/(3y/8). Then isolate the new A rate and solve from there.
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.