Second container is being filled faster
Solution:
To determine which container is being filled faster, we have to find the unit rate
Unit rate = Number of gallons filled in 1 minute
Liquid enters the first container at a rate of 2/3 gallon per 1/4 minute
[tex]\frac{1}{4} \text{ minute } = \frac{2}{3} \text{ gallons }[/tex]
To find the number of gallons filled in 1 minute, multiply both the sides of above equation by 4
[tex]\frac{1}{4} \times 4 \text{ minute } = \frac{2}{3} \times 4 \text{ gallons }\\\\1 \text{ minute } = \frac{8}{3} \text{ gallons } = 2.67 gallons[/tex]
Thus unit rate of first container is 2.67 gallons per minute
Liquid pours into the second storage container at a rate of 3/5 gallon per 1/6 minute
[tex]\frac{1}{6} \text{ minute } = \frac{3}{5} \text{ gallons }[/tex]
To find the number of gallons filled in 1 minute, multiply both the sides of above equation by 6
[tex]\frac{1}{6} \times 6 \text{ minute } = \frac{3}{5} \times 6 \text{ gallons }\\\\1 \text{ minute } = \frac{18}{5} \text{ gallons } = 3.6 \text{ gallons }[/tex]
Thus unit rate of second container is 3.6 gallons per minute
On comparing the unit rate of both containers we find,
3.6 > 2.67
second container > first container
Thus second container is being filled faster
