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10 October, 14:08

Suppose a bucket is placed under two faucets. If one faucet is turned on alone, the bucket will be filled in 6 minutes. If the other faucet is turned on alone the bucket will be filled in 4 minutes. What fraction of the bucket will be filled in one minute if both faucets are turned on at the same time?

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  1. 10 October, 15:31
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    So let's call the faucet that can fill the bucket in 6 minutes faucet 1, and the other one faucet 2.

    So here, it's asking about if the faucet was turned on for a minute.

    So let's find the amount of the bucket that each faucet can fill in a minute.

    Faucet one can fill a bucket in 6 minutes, so therefore if it was only one minute it could fill 1/6 of a bucket.

    Faucet two can fill a bucket in 4 minutes, so therefore if it was only one minute it could fill 1/4 of a bucket.

    So if both of them are turned on, then we just have to add the two fractions together.

    To add 1/4 and 1/6, convert them both two have the same denominator.

    The easiest number would be to switch them both to have a denominator of 12.

    So to do that, for 1/6, just multiply by 2/2, to get 2/12, and for 1/4, just multiply by 3/3, to get 3/12.

    So 2/12 + 3/12 is 5/12.

    So 5/12 of the bucket will be filled in a minute if both faucets are turned on at the same time.
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