Graph Analysis: Finding the 24-Liter Mark in Bowl A's Water Level

Q: How do I know which line represents bowl A?

Look at the starting points! Bowl A starts empty (0 liters) so its line begins at the bottom. Bowl B starts with 32 liters, so its line begins higher up on the graph.

Q: What if the line doesn't pass exactly through a grid intersection?

Use your best estimate by looking at the closest grid lines. In this problem, the line clearly passes through exact values, making it easy to read precisely.

Q: Why do both lines go up at different rates?

The lines have different slopes because the bowls fill at different rates. Bowl A fills faster (steeper line) while Bowl B fills more slowly since it already contains water.

Q: What does the intersection of the two lines mean?

The intersection shows when both bowls contain the same amount of water. This happens around 16 minutes when both have approximately 48 liters.

Linear Graph Interpretation with Time-Volume 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 there be 24 liters of water in the tank A?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

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 there be 24 liters of water in the tank A?

Step-by-step solution

To solve this problem, we will analyze the graph provided:

The problem states that bowl A starts empty and we need to find out when it reaches 24 liters of water. Observing the graph:

The line representing bowl A starts at 0 liters.
Locate the point where the line meets the 24-liter mark on the vertical scale (y-axis).
From this intersection, move down vertically to the horizontal scale (x-axis) to read the corresponding time in minutes.

According to the graph, when bowl A contains 24 liters of water, the corresponding time is 10 minutes.

Therefore, the answer to the problem is $10$ minutes.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Find 24 liters on y-axis, trace horizontally to line A
Technique: From intersection point, drop vertically down to x-axis at 10 minutes
Check: Verify line A passes through (10, 24) on the coordinate plane ✓

Common Mistakes

Avoid these frequent errors

Reading the wrong line or confusing bowl A with bowl B
Don't follow line B which starts at 32 liters = reading bowl B's water level instead! Line B represents the bowl that starts full. Always identify line A which starts at 0 liters and increases over time.

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:

FAQ

Everything you need to know about this question

How do I know which line represents bowl A?

Look at the starting points! Bowl A starts empty (0 liters) so its line begins at the bottom. Bowl B starts with 32 liters, so its line begins higher up on the graph.

What if the line doesn't pass exactly through a grid intersection?

Use your best estimate by looking at the closest grid lines. In this problem, the line clearly passes through exact values, making it easy to read precisely.

Why do both lines go up at different rates?

The lines have different slopes because the bowls fill at different rates. Bowl A fills faster (steeper line) while Bowl B fills more slowly since it already contains water.

Can I solve this algebraically instead of using the graph?

Yes! You could find the equation of line A and substitute 24 for the water level, but the graph method is faster and more visual for this type of problem.

What does the intersection of the two lines mean?

The intersection shows when both bowls contain the same amount of water. This happens around 16 minutes when both have approximately 48 liters.

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