Sumanta needs to type up her 1950-word paper by its 5 pm deadline. If she starts at least two hours in advance, her typing speed will be a constant 20 words per minute, but for every two minutes beyond 3 pm that she waits before starting, her constant typing speed will increase by one word per minute. What is the latest time at which Sumanta can begin typing in order to finish her paper by the deadline?
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This one took me way too long. The trap is that speeding up might make starting later actually better — took me a while to see the optimization part.
Same here. I kept plugging in answer choices from the top and it worked but felt slow. Is there a faster way to set it up?
Wait, why is the speed increase 'for every two minutes beyond 3 pm' but the answer choices go up to 4:42? Doesn't it say she starts at least two hours in advance for the 20 wpm?
If she starts before 3, she just gets the flat 20 wpm. The interesting part is between 3 and 5.
Respect for anyone who gets this right under 2 min. 705+ for sure. I got 3:30 by checking 1950/... wait can't say more, but I'm not confident.
I'm between two of the middle answers. The units (words per minute vs every two minutes) are what's killing me.
Quick note: the answer hinges on comparing total time including the delay vs the speed boost. Don't forget the remaining time shrinks as she waits.
This is the key insight, thank you. I was only looking at speed, not the shrinking window.
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.