Ashley can finish a job in days and Barbara can do the same work in days. Ashley worked for days and left the job. In how many days, Barbara alone can finish the remaining work?
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Wait, I keep getting 6 days but that's not matching... let me recheck. Ashley does 10/15 = 2/3 of the job, so 1/3 is left. Barbara's rate is 1/18 per day, so (1/3)/(1/18) = 6. Oh, that IS option B. I second-guessed myself for nothing lol.
Haha same, I got 6 and then stared at the choices like something was wrong 😅
Nice, that 2/3 shortcut is way faster than doing the full fraction math.
Got B pretty quickly. This one felt easier than most rate problems since the leftover work is a clean fraction.
Yeah 1/3 leftover makes it smooth. If the numbers were uglier this would've taken me longer.
Can someone explain why we don't just add their rates together? I always get confused about when to combine rates vs when they work separately.
Because Ashley LEAVES after 10 days. So they're not working together the whole time — only Ashley works first, then only Barbara.
Ashley working 10 out of 15 days is the key detail here. Once you see 1/3 of the job remains, it's basically a one-person rate problem.
Exactly, the trick is not overcomplicating it with combined rates.
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.