Question

an empty bucket is put under two faucets. if one faucet is turned on alone, the bucket fills in 6 minutes.if the other faucet is turned on, it fills in 4 minutes. if both are turned on, how many seconds will it take to fill the bucket?

Answer 1

Let x be the answer
Make this chart:

buckets filled time rate in buckets/minute
1st faucet 1 6
2nd faucet 1 4
both open 1 x

Fill in the rates by dividing buckets by minutes:

buckets filled time rate in buckets/minute
1st faucet 1 6 1/6
2nd faucet 1 4 1/4
both faucets 1 x 1/x


Equation:

1st faucet's rate + 2nd faucet's rate = their combined rate:

1/6 + 1/4 = 1/x

Multiply through by 12x

2x + 3x = 12
5x = 12
x = 2.4 minutes.