Linear Function Analysis: Calculate Time to Fill Bowl B Using Water Level Graph

Q: How do I know which line represents Bowl B?

Look for the line that starts at 32 liters on the y-axis (Water Level). Bowl B begins with 32 liters of water, while Bowl A starts empty at 0 liters.

Q: What does it mean when the line levels off?

When a line becomes horizontal or flat, it means the bowl has reached its maximum capacity and is full. No more water can be added, so the level stays constant.

Q: Why are there two different lines on the graph?

Each line represents a different bowl. The lower line starting at 0 is Bowl A (starts empty), and the upper line starting at 32 is Bowl B (starts with water).

Q: How do I read the time when the bowl is full?

Find where Bowl B's line reaches its highest point and levels off. Draw an imaginary vertical line down to the x-axis (Time) to read the exact minute value.

Q: What if I read the graph wrong and get 22 minutes?

Double-check that you're following the correct line for Bowl B and reading where it truly levels off. The line should reach its peak and stay flat at exactly 20 minutes.

Graph Analysis with Linear Rate Interpretation

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 B bowl be full?

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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 the B bowl be full?

Step-by-step solution

To solve this problem, let's follow these steps:

Step 1: Identify the line corresponding to bowl B on the graph. This is typically marked and will indicate the initial amount of water (32 liters).
Step 2: Observe the line's trajectory as time proceeds. Bowl B starts with 32 liters, so we look for the line that begins at this level on the vertical axis.
Step 3: The graph line for bowl B will gradually increase as time passes through minute intervals. Find the time at which this line reaches the top level, signifying maximum capacity (full).

Upon examining the graph:

Bowl B's line starts at 32 liters and continues to rise. At the 20-minute interval mark on the time axis, the trajectory for bowl B reaches its peak level and levels off, indicating the bowl is full.

Therefore, the solution to the problem is $20$ minutes.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Graph Reading: Identify correct line and starting water level from y-axis
Technique: Follow Bowl B line from 32 liters to maximum capacity point
Check: Verify line reaches peak at time = 20 minutes on x-axis ✓

Common Mistakes

Avoid these frequent errors

Confusing Bowl A and Bowl B lines on the graph
Don't follow the wrong line that starts at 0 liters = wrong bowl analyzed! Bowl A starts empty while Bowl B starts with 32 liters. Always identify which line corresponds to Bowl B by checking the starting water level matches 32 liters.

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 B?

Look for the line that starts at 32 liters on the y-axis (Water Level). Bowl B begins with 32 liters of water, while Bowl A starts empty at 0 liters.

What does it mean when the line levels off?

When a line becomes horizontal or flat, it means the bowl has reached its maximum capacity and is full. No more water can be added, so the level stays constant.

Why are there two different lines on the graph?

Each line represents a different bowl. The lower line starting at 0 is Bowl A (starts empty), and the upper line starting at 32 is Bowl B (starts with water).

How do I read the time when the bowl is full?

Find where Bowl B's line reaches its highest point and levels off. Draw an imaginary vertical line down to the x-axis (Time) to read the exact minute value.

What if I read the graph wrong and get 22 minutes?

Double-check that you're following the correct line for Bowl B and reading where it truly levels off. The line should reach its peak and stay flat at exactly 20 minutes.

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