Question

One tank is filling at at a rate of 3/4 gallon per 2/3 minutes. A second tank is filling at a rate of 5/8 gallon per 1/2 minutes. Which tank is filling faster?

Answer 1

3/4 times 3/2 (reciprocal of the second fraction) is 9/8 gallons per minute.
5/8 times 2/1 (reciprocal of the second fraction) is 10/8 gallons per minute

The second tank is filling faster.

Answer 2

Explanation:

Given

First tank is filling at a rate of
`(3)/(4)` gallon per
`(2)/(3)` minute i.e. per 40 sec

In 1 sec it fills
`(3)/(4* 40)=(3)/(160) gallon`

For second tank

Filling at a rate of
`(5)/(8) per (1)/(2) minutes`

i.e. per 30 sec

in 1 sec it fills
`(5)/(8* 30)=(5)/(240)`

`(5)/(240)>{3}{160}`

thus second tank is filling at a faster rate.