Graph Analysis: Finding Bowl A's Fill Time with 32-Liter Initial Condition

Graph Interpretation with Linear Rate Analysis

Given two bowls A and B

The bowl A emptand and the bowl B contains 32 liters of water.

We fill the bowls with water until theand are full, here is a graph showing the amount of water in the two bowls as a function of time

After how manand minutes from the time the taps are opened, will the A bowl be full?

Time222444666888101010121212141414161616181818202020222222242424262626282828303030Water Level888161616242424323232404040484848565656646464727272808080888888969696104104104112112112000AB

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given two bowls A and B

The bowl A emptand and the bowl B contains 32 liters of water.

We fill the bowls with water until theand are full, here is a graph showing the amount of water in the two bowls as a function of time

After how manand minutes from the time the taps are opened, will the A bowl be full?

Time222444666888101010121212141414161616181818202020222222242424262626282828303030Water Level888161616242424323232404040484848565656646464727272808080888888969696104104104112112112000AB

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information and analyze the graph to understand the data.
  • Step 2: Determine which line corresponds to Bowl A and find where it reaches maximum filling on the graph.
  • Step 3: Note the time at which the line reaches maximum capacity to solve when Bowl A is full.

Now, let's work through each step:

Step 1: We start by examining the graph. The graph shows two lines, one for each bowl. The vertical axis indicates the amount of water, while the horizontal axis indicates time in minutes.

Step 2: Identify the line that represents Bowl A. From the graph, we find that the line starting at zero represents Bowl A since Bowl B starts at 32 liters.

Step 3: We observe that the line for Bowl A reaches its maximum level on the graph at a time corresponding to 20 minutes. At this point, the line becomes horizontal, indicating the bowl is full.

Therefore, the solution to the problem is 20 minutes.

3

Final Answer

20

Key Points to Remember

Essential concepts to master this topic
  • Reading Graphs: Identify which line represents each bowl by starting values
  • Finding Maximum: Bowl A reaches 112 liters at time = 20 minutes
  • Verification: Line becomes horizontal when bowl is full at 20 minutes ✓

Common Mistakes

Avoid these frequent errors
  • Confusing which line represents Bowl A
    Don't assume the upper line is Bowl A = wrong bowl analyzed! Bowl B starts at 32 liters (upper position), while Bowl A starts empty at 0 liters. Always check the starting water levels to identify the correct line.

Practice Quiz

Test your knowledge with interactive questions

Look at the graph below and determine whether the function's rate of change is constant or not:

–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777888999101010111111–3–3–3–2–2–2–1–1–1111222333444555000

FAQ

Everything you need to know about this question

How do I know which line is Bowl A and which is Bowl B?

+

Look at the starting points at time = 0! Bowl A starts empty (at 0 liters), so it's the line beginning at the bottom. Bowl B starts with 32 liters, so it's the line starting higher up.

What does it mean when the line becomes horizontal?

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A horizontal line means the water level stops changing - the bowl is completely full! No more water can be added, so the line stays flat at maximum capacity.

Why does Bowl A fill faster than Bowl B?

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Bowl A has a steeper slope on the graph, meaning water is being added at a faster rate. The steeper the line, the faster the filling rate!

How can I double-check my answer from the graph?

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Find where Bowl A's line becomes horizontal and trace straight down to the time axis. Also verify that Bowl A reaches approximately 112 liters (same as Bowl B's final level).

What if I read the wrong time value?

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Make sure you're reading the exact point where the line stops rising. Use the grid lines to help - the line becomes horizontal right at the 20-minute mark on the time axis.

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