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Solution to CyberTeaser B293

There are two possible cases: (a) the smaller tank is filled first from the less powerful hose, or (b) it is filled first from the more powerful hose. Let us work with case (a) first. In this case, it will take 6.3/2.9 minutes to fill the first half of the small container, during which the larger container receives (6.5/2.9)(8.7) liters of water. Then it will take 6.3/8.7 minutes to fill the second half of the small container, and the same amount to top off the larger one (because the jobs are completed at the same time). So the larger container, during this time, receives (6.3/8.7)(2.9) liters of water. Since this fills the larger container, it must contain

(6.3/2.9)(8.7) + (6.3/8.7)(2.9) = 21 liters.

Case (b) is left for the reader, who may notice that it requires exactly the same arithmetic as case (a).

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