Question

a pump fills a pool at a constant rate. at the end of 3 minutes it has filled 2 gallons of water. which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
a

time (minutes)	water (gallons)
7	5
8	6

b

time (minutes)	water (gallons)
6	6
9	8

c

time (minutes)	water (gallons)
6	5
12	11

d

time (minutes)	water (gallons)
9	6
15	10

Explanation:

Step1: Find the rate

The pump fills 2 gallons in 3 minutes, so the rate is $\frac{2}{3}$ gallons per minute.

Step2: Check each table

• For Table A: From 6 to 7 minutes (1 minute), water goes from 4 to 5 (1 gallon), rate is 1, not $\frac{2}{3}$.
• For Table B: From 3 to 6 minutes (3 minutes), water goes from 2 to 6 (4 gallons), rate is $\frac{4}{3}$, not $\frac{2}{3}$.
• For Table C: From 3 to 6 minutes (3 minutes), water goes from 2 to 5 (3 gallons), rate is 1, not $\frac{2}{3}$.
• For Table D: From 6 to 9 minutes (3 minutes), water goes from 4 to 6 (2 gallons), rate is $\frac{2}{3}$. From 9 to 15 minutes (6 minutes), water goes from 6 to 10 (4 gallons), rate is $\frac{4}{6}=\frac{2}{3}$. Also, at 6 minutes, water should be $6\times\frac{2}{3}=4$, which matches. At 9 minutes, $9\times\frac{2}{3}=6$, matches. At 15 minutes, $15\times\frac{2}{3}=10$, matches.

Answer:

D. Time (minutes) | Water (gallons); 6 | 4; 9 | 6; 15 | 10