At a constant rate of flow, it takes minutes to fill a swimming pool if a large hose is used and minutes if a small hose is used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
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Thanks, this one finally made combined rates click for me. I kept trying to average 20 and 30 in my head and kept getting confused.
Same here! Averaging the times is the classic trap.
Yep, add the rates, not the times. Took me a while too.
Quick question: how do you know to use 1/20 and 1/30 instead of just adding 20+30? I get it now but want to be sure I don't mess this up under pressure.
Think of it as pools per minute — the large hose does 1/20 of the pool each minute.
Once you see it as "work per minute," adding the fractions feels natural.
Sub-505 but I still overthought it for a solid minute. The numbers are friendly enough that the answer is clearly less than 20.
Yeah, any combined rate has to beat the faster hose alone, so 10 or 12 are the only real candidates.
Nice, straightforward work-rate problem. Adding the rates gives 1/20 + 1/30, then flip it. Took me about 30 seconds.
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.