Two taps can fill a cistern in 20 minutes and 30 minutes. The first tap was opened initially for x minutes after which the second tap was opened. If it took a total of 15 minutes for the tank to be filled, what is the value of x?
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Got 10, but I set it up as combined work for the remaining 15-x minutes. Is that the intended approach?
Yeah, that's how I did it too. First tap alone for x, then both together for the rest.
Same here. Once you see the two phases it's pretty quick.
This one tripped me up because I kept thinking the 15 minutes was only for the second tap. Thanks for posting!
Classic trap. The 15 is total time from the very start.
605-655 feels right. Not hard once you write the equation, but the wording takes a sec to parse.
Quick note: first tap fills 1/20 per minute and second fills 1/30, so together they do 1/12. That fraction made the algebra cleaner for me.
Nice, 1/12 is way easier to work with than dealing with 20 and 30 directly.
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.