Question

full of water. then, she pours a steady stream of water on the flowers. when the watering can is empty, she walks to the outdoor faucet at the back of her house and refills it. which graph could show the amount of water in the watering can over time?

Explanation:

Step1: Analyze the process

The watering can starts full (so initial volume is high). Then, as she pours water on flowers, the volume decreases steadily until the can is empty. After that, she walks to the faucet and refills it. When refilling, the volume should increase rapidly (since it's a steady stream to refill, but the time to walk and refill: when refilling, the volume goes from 0 to full quickly, and then? Wait, no: wait, the process is: starts full, pours (volume decreases linearly to 0), then walks to faucet (time passes, volume stays 0), then refills (volume increases rapidly to full). Wait, no, the problem says "when the watering can is empty, she walks to the outdoor faucet... and refills it". So after emptying, there's a period (walking) where volume is 0, then refilling (volume goes up quickly to full). Wait, but let's check the graphs.

Wait, first phase: starts full, volume decreases linearly to 0 (so a line with negative slope from high y to (x1, 0)). Second phase: empty, so volume is 0 for some time (horizontal line at y=0). Third phase: refills, so volume increases rapidly (vertical or steep line) back to full (same as initial y). Now let's check the graphs:

First graph: after emptying, it goes up to full and stays? No, because after refilling, does she stop? Wait, the problem says "when the watering can is empty, she walks to... and refills it". So after refilling, what? Wait, maybe the refilling is instantaneous? No, but the key is the shape.

Wait, let's list the graphs:

Top left: starts high, decreases to 0, then increases back to high (steep line) and stays? No, the second part is a steep increase to high, then horizontal. But after refilling, does she use it again? The problem doesn't say. Wait, maybe the process is: full -> pour (decrease to 0) -> refill (increase to full) -> maybe stop? But the graphs:

Top right: starts high, decreases to 0, stays 0 for a while, then increases to high (steep line). That matches: full (high y), pour (decrease to 0, linear), then walk (volume 0, horizontal), then refill (increase to high, steep). Wait, but let's check the other graphs.

Wait, the first graph (top left): after decreasing to 0, it increases back to high and stays. But the problem says "when the watering can is empty, she walks to... and refills it". So after emptying, she refills it. So the sequence is:

1. Initial state: full (volume = max).
2. Pouring: volume decreases linearly to 0 (time passes, volume goes down).
3. Empty: volume = 0, and she walks to faucet (time passes, volume remains 0).
4. Refilling: volume increases rapidly to max (since she refills it).

Now, looking at the graphs:

- Top left: after 0, increases to max and stays. But does she start using it again? The problem doesn't say, but maybe the refilling is to full, and then maybe the graph ends? Wait, no, the question is which graph could show the amount over time.

Wait, let's check the top right graph:

- Starts high (full), decreases linearly to 0 (negative slope), then stays 0 (horizontal line), then increases rapidly to high (positive steep slope). That matches the process: full -> pour (decrease to 0) -> walk (volume 0) -> refill (increase to full).

Wait, but the top left graph: after decreasing to 0, it increases to full (steep line) and then stays. But the problem doesn't say she uses it again. But maybe the refilling is to full, and then the graph stops? Wait, maybe I misread. Let's re-examine the problem: "Which graph could show the amount of water in the watering can over time?"

Let's analyze each graph:

1. Top left: starts high, decreases to 0, then increases to high (steep) and stays. But after refilling, does she use it? The problem doesn't mention, but maybe the refilling is the end. But the process is: full -> pour (decrease) -> empty -> refill (increase). So the graph should have: high -> decrease to 0 -> (maybe a pause) -> increase to high.

Top right: high -> decrease to 0 -> stay 0 -> increase to high. That's correct because after emptying, she walks (time passes, volume 0) then refills (volume up).

Wait, but let's check the other graphs:

Bottom left: starts at 0, increases to high, then decreases to 0. No, initial volume is full, so this is wrong.

Bottom right: starts at 0, increases to high, stays, then decreases to 0. Also wrong, initial volume is full.

So the correct graph is the top right? Wait, no, wait the top left: after decreasing to 0, it goes up to high (steep) and stays. But the top right: after decreasing to 0, stays 0, then goes up. Which is correct?

Wait, the key is: when she refills, does she take time to walk? So between emptying and refilling, there's a time when the can is empty (volume 0) while she walks. So the graph should have a horizontal segment at y=0 between the decreasing line and the increasing line.

Looking at the top right graph: first, a line decreasing from high to 0 (linear), then a horizontal line at 0 (time when she walks), then a steep line increasing to high (refilling). That matches.

Wait, but the top left graph: after decreasing to 0, it immediately increases to high (no horizontal segment). But the problem says "when the watering can is empty, she walks to the outdoor faucet... and refills it". So "walks" implies some time passes (so volume is 0 for a while) before refilling. So the top right graph has a horizontal segment at 0, then increases. So that's the correct one.

Wait, but let's check the axes. The y-axis is volume (dt.), x-axis is time (sec.). So:

- Initial: (0, V_max)
- Pouring: line from (0, V_max) to (t1, 0), slope negative.
- Walking: from t1 to t2, volume 0 (horizontal line y=0).
- Refilling: from t2 to t3, volume increases from 0 to V_max (steep line, since refilling is quick), so at t3, volume is V_max.

So the graph should have:

- Decreasing line to 0.
- Horizontal line at 0.
- Increasing line to V_max.

Looking at the top right graph: yes, that's exactly it. The top left graph has no horizontal line at 0; it goes from 0 to V_max immediately, which would mean no time to walk, just refill instantly. But the problem says she walks to the faucet, so there's a time when volume is 0. So the top right graph is correct.

Wait, but maybe I made a mistake. Let's check again. The problem says "when the watering can is empty, she walks to the outdoor faucet at the back of her house and refills it". So after emptying, she walks (time passes, volume 0) then refills (volume goes up). So the graph should show:

1. Volume starts high, decreases linearly to 0 (time t1).
2. Volume remains 0 from t1 to t2 (walking time).
3. Volume increases rapidly to high at t2 (refilling).

So the graph with a decreasing line to 0, then a horizontal line at 0, then an increasing line to high is the top right graph.

Step2: Match with the graphs

Looking at the options:

Top right graph:

- Starts at high y (full), decreases to 0 (linear, negative slope).
- Then, a horizontal segment (y=0) for some time (walking).
- Then, a steep increase (positive slope) back to high y (refilled).

Yes, that matches the process. So the correct graph is the top right one (second graph in top row).

Answer:

The graph in the top right (the second graph in the top row) which shows volume starting high, decreasing linearly to 0, staying at 0 for a period, then increasing rapidly back to high.