A local dairy has three machines to fill half-gallon milk cartons. The machines can fill the daily quota in 6 hours, 7 hours, and 7.5 hours, respectively. Find how long it takes to fill the daily quota if all three machines are running.

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Equation:

rate + rate + rate = together rate

1/6 + 1/7 + 2/15 = 1/x

Multiply thru by 630x to get:

105x + 90x + 84x = 630

279x = 630

x = 2.26 hrs