Answer:
10/3 gallons/minute
Step-by-step explanation:
There are 4 quarters in 1, so four quarter-minutes in one minute.
The the number of gallons going into buckets in one minute will be 4 times the number in 1/4 minute:
... 4 × 5/6 gal = 20/6 gal = 10/3 gal
This is the quantity per minute, so the unit rate is
... 10/3 gal/min
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<em>Alternate solution</em>
You are asked for the rate in gallons per minute. In this context, "per" means "divided by", so you find the desired quantity by dividing gallons by minutes.
... (5/6 gal)/(1/4 min) = (5/6×4/1) gal/min = 10/3 gal/min
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<em>Comment on dividing fractions</em>
You're generally taught one or two ways to divide fractions:
- invert the denominator and multipy: (5/6)/(1/4) = (5/6)×(4/1) = 20/6 = 10/3.
- express both over a common denominator, then lose the denominator: (5/6)/(1/4) = (10/12)/(3/12) = 10/3
Please note that if you invert and multiply after doing the adjustment in the second method, you would have (10/12)×(12/3) = (10/3)×(12/12) = 10/3. That is, the denominators cancel. It's just another way to think about the quotient of fractions.
There's actually a third method you can use, but you need to be really careful.
3. Express both fractions using the same numerator, then invert the result after losing the numerator: (5/6)/(1/4) = (5/6)/(5/20) = 20/6 = 10/3. Again, this is a variation that takes advantage of cancellation after "invert and multiply."
