Question

One tank is filling at a rate of 5/8 gallon per 7/10 hour. A second tank is filling at a rate of 5/9 gallon per 2/3 hour. Which tank is filling faster? Explain how you know.

Answer 1

First recognize that the unit rate we're finding is gallons per hour, or
`(g)/(h)`.

rate for Tank 1 = x gallons per hour = a gallons / b hours


`T_(1)=((5)/(8))/((7)/(10))\\\\T_(1)=(5)/(8)*(10)/(7)\\\\T_(1)=(50)/(56)\\\\\\Fill\ rate\ of\ Tank\ 1=(25)/(28)`


rate for Tank 2 = y gallons per hour = c gallons / d hours


`T_(2)=((5)/(9))/((2)/(3))\\\\T_(2)=(5)/(9)*(3)/(2)\\\\T_(2)=(15)/(18)\\\\T_(2)=(15)/(18)\\\\\\Fill\ rate\ of\ Tank\ 2=(5)/(6)`