An empty bucket put under two faucets. If one faucet is turned on alone,the bucket fills in 6 minutes.if the other faucet is turned on alone,the bucket fills in 4 minutes.if both are turned on,how many seconds will it take to fill the bucket?
Two ways, with and without algebra:
Without algebra:
In 12 minutes the first faucet can fill 2 buckets while the second one
fills 3 buckets. That's 5 buckets in 12 minutes or 1 bucket in 12÷5
or 2.4 minutes.
With algebra:
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.
It's easier without algebre, but I assume you are taking algebra.
Edwin