The Hose Knows

This is a fairly straight-forward Brainteaser from the Quantum magazine.

“A man is filling two tanks with water using two hoses. The first hose delivers water at the rate of 2.9 liters per minute, the second at a rate of 8.7 liters per minute. When the smaller tank is half full, he switches hoses. He keeps filling the tanks, and they both fill up completely at the same moment. What is the volume of the larger tank if the volume of the smaller tank is 12.6 liters?”

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