Two liquid storage containers are being filled. Liquid enters the first container at a rate of 2/3 gallon per 1/4 minute. Liquid pours into the second storage container at a rat…

Question

asked Dec 23, 2021 204k views

2 Answers

Mapping Dom · Answer 1 · 2021-12-30T12:24:50+0000

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

$(1)/(4) \text{ minute } = (2)/(3) \text{ gallons }$

To find the number of gallons filled in 1 minute, multiply both the sides of above equation by 4

$(1)/(4) * 4 \text{ minute } = (2)/(3) * 4 \text{ gallons }\\\\1 \text{ minute } = (8)/(3) \text{ gallons } = 2.67 gallons$

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

$(1)/(6) \text{ minute } = (3)/(5) \text{ gallons }$

To find the number of gallons filled in 1 minute, multiply both the sides of above equation by 6

$(1)/(6) * 6 \text{ minute } = (3)/(5) * 6 \text{ gallons }\\\\1 \text{ minute } = (18)/(5) \text{ gallons } = 3.6 \text{ gallons }$

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