If both valves are open simultaneously, they can fill an empty pool in 48 minutes. The first valve, when working independently, takes 2 hours to fill the pool. If the second valve releases 50 cubic meters of water more than the first valve every minute, what is the capacity of the pool?
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Took me a minute to realize I needed to convert the 2 hours to 120 minutes before doing anything else. Classic unit trap.
Same here, I almost used 2 directly in the rate equation 😅
Yeah, always convert to the same time unit first. Saved me on similar problems.
Got D. The key was setting up the combined rate as 1/48 and first valve as 1/120, then figuring out the second valve's rate.
How did you go from the rates to the cubic meters part? That's where I got stuck.
This one was a nice mix of rates and a bit of algebra. Not too bad once you see the structure, but the 50 m³ difference tripped me up at first.
Is there a shortcut here? I ended up doing the full equation but it felt longer than it should be for a 605-655 level question.
You can also think of it as the second valve doing 1/48 - 1/120 of the pool per minute, then relate that fraction to the 50 m³ difference. Still algebra but maybe cleaner.
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.