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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Alternate solution
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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Comment on dividing fractions
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."
