Pump A, pumping water at a constant rate, can fill a certain swimming pool in 6 hours. Pump B, pumping water at a constant rate, can fill the same pool in 4 hours. If both pumps begin filling the pool simultaneously when the pool is empty and pump B breaks down 1 hour after they begin filling the pool, how many hours will it take pump A alone to finish filling the pool?
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Thanks, this one clicked for me after I drew a quick table. Classic combined rate problem.
Wait, why do we subtract the 1 hour from the remaining work instead of just adding it at the end? I keep getting confused on what portion of the pool is already filled.
Think about what both pumps accomplish together in that first hour, then what's left for A alone.
Medium difficulty for me. The trick is noticing B only works for 1 hour, so you can't just use the combined rate for the whole job.
Exactly, that 1-hour detail is the whole trap.
Got B, but I almost picked C because I forgot to subtract the work already done. Good reminder to always track remaining work.
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.