Question

choose the correct answer. a faucet fills a 9 gallon tank in 3 minutes. \\(\frac{9\text{ gal}}{3\text{ min}}\\) which graph describes this ratio? hint: use the unit rate!

Explanation:

Step1: Calculate unit rate

The faucet fills 9 gallons in 3 minutes. The unit rate (gallons per minute) is $\frac{9}{3} = 3$ gallons per minute. So, at 1 minute, volume is 3 gal; at 2 minutes, 6 gal; at 3 minutes, 9 gal.

Step2: Analyze graphs

• First graph: Check points. At 2 min, volume should be 6? Wait, no, wait. Wait, first graph: let's see x (time) and y (volume). Let's check coordinates. Wait, first graph: when x=2, y=3? No, wait, no. Wait, unit rate is 3 gal per min. So at x=1, y=3; x=2, y=6; x=3, y=9. Wait, second graph: let's see. Wait, maybe I misread. Wait, the first graph: let's check the points. Wait, maybe the second graph has at x=2, y=6? Wait, no, the middle graph (second one) – wait, the three graphs: left, middle, right. Wait, the unit rate is 3 gal/min. So the graph should have a slope of 3. Let's check the middle graph: when x=1, y=3; x=2, y=6? Wait, no, maybe the first graph: wait, the left graph: at x=2, y=3? No, that's slope 1.5. Wait, no, wait the calculation: 9 gal in 3 min, so rate is 3 gal/min. So the correct graph should pass through (1,3), (2,6), (3,9). Let's check the middle graph: if at x=1, y=3; x=2, y=6? Wait, maybe the middle graph (second one) has those points. Wait, the left graph: let's see, at x=2, y=3? No, that's 1.5. The middle graph: when x=1, y=3; x=2, y=6? Wait, maybe the middle graph is the one with steeper slope. Wait, the right graph has a shallow slope, so that's out. The left graph: let's check the points. Wait, maybe I made a mistake. Wait, the first graph: let's see, the x-axis is time (min), y-axis volume (gal). Let's take the first graph: when x=2, y=3? No, that's 1.5 gal per min. The middle graph: when x=1, y=3; x=2, y=6? Yes, that's 3 gal per min. Wait, no, wait the problem says 9 gal in 3 min, so at 3 min, 9 gal. So the graph should have (3,9). Let's check the middle graph: if at x=3, y=9? Wait, maybe the middle graph is the correct one. Wait, no, wait the first graph: let's see, the left graph: when x=3, y=9? Wait, maybe I misread. Wait, the left graph: let's check the points. Suppose the left graph has (2,3), (4,6) – no, that's slope 1.5. The middle graph: slope 3. The right graph: slope 1. So the correct graph is the middle one (second graph) because it has a slope of 3 (3 gal per min), passing through (1,3), (2,6), (3,9).

Answer:

The Middle Graph