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?

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.