Cat Rat Dash

Starting from point \(P\), a cat was running in a bigger circular road with circumference of 36 feet while a rat was running in a smaller circular one with circumference of 24 feet. Both of them would continue their trip in each of their circle until they met up at point \(P\) again: the cat would finally catch the rat.

If the cat's velocity was 7 feet/second, and the rat's velocity 5 feet/second, then in how many seconds would they meet at point \(P\)?


Inspired by Japanese Sangaku
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