Question

Three co-workers recorded the amount of water in a fish tank being replaced at regular intervals.

maggie measured 1/2 gallon of water in 2/3 of an hour.

christine measured 3/4 gallon of water in 6/5 of an hour.

gianna measured 2/3 gallons of water in 4/5 of an hour.


What two statements are true?

A. Giannas fish tank replaced the most water per hour.

B. Christies fish tank replaced the most water per hour.

C. Christies fish tank replaced the least water per hour.

D. All three fish tank replaced more than one gallon of water per hour.

E. Two of the fish tanks almost replaced the same amount of water per hour.

Answer 1

A. Giannas fish tank replaced the most water per hour.

C. Christies fish tank replaced the least water per hour.

Explanation:

Let define the replacement rate (
`r`), measured in gallons per hour, by the ratio of capacity (
`c`), measured in gallons, to replacing time (
`t`), measured in hours. That is:

`r = (c)/(t)` (1)

The co-worker with the highest rate replaces the most water in a hour. Let see the rate of each co-worker:

Maggie (
`c = (1)/(2)\,gal`,
`t = (2)/(3)\,h`)

`r = ((1)/(2)\,gal )/((2)/(3)\,h )`

`r = (3)/(4)\,(gal)/(h)`

`r = 0.75\,(gal)/(h)`

Christine (
`c = (3)/(4)\,gal`,
`t = (6)/(5)\,h`)

`r = ((3)/(4)\,gal )/((6)/(5)\,h )`

`r = (15)/(24)\,(gal)/(h)`

`r = (5)/(8)\,(gal)/(h)`

`r = 0.625\,(gal)/(h)`

Gianna (
`c = (2)/(3)\,gal`,
`t = (4)/(5)\,h`)

`r = ((2)/(3)\,gal )/((4)/(5)\,h )`

`r = (10)/(12)\,(gal)/(h)`

`r = (5)/(6)\,(gal)/(h)`

`r = 0.833\,(gal)/(h)`

From these informations, we conclude that Gianna's fish tank replaced the most water per hour and Christine replaced the least water per hour. All three fish tanks replace less than one gallon of water per hour. Therefore, correct answers are A and C.