Graph Analysis: Finding Water Levels in Two Bowls After 10 Minutes

Q: How do I tell which line represents which bowl?

Look at the starting points at time 0! Bowl A starts at 0 liters (bottom line), while Bowl B starts at 32 liters (upper line). The graph also labels them as A and B.

Q: What if the lines don't pass exactly through grid points?

Estimate as closely as possible! Look at the nearest grid lines and interpolate between them. For this problem, the lines pass through clear points at 10 minutes.

Q: Why does Bowl B start with water while Bowl A is empty?

This is given in the problem setup! Bowl A starts empty and Bowl B starts with 32 liters. Always read the initial conditions carefully.

Q: Do both bowls fill at the same rate?

No! Look at the slopes of the lines. Bowl A fills faster (steeper line) while Bowl B fills slower (gentler slope). The rates are different for each bowl.

Graph Interpretation with Linear Water Filling

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

How manand liters of water are in each container after 10 minutes of pumping the water?

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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

How manand liters of water are in each container after 10 minutes of pumping the water?

Step-by-step solution

We start by interpreting the graph to find the water levels in bowls A and B at 10 minutes:

Initially, Bowl A contains 0 liters, and Bowl B contains 32 liters of water.
According to the graph, as time progresses, both bowls experience changes in water levels.
After 10 minutes, check the vertical representation on the graph for the water level in each bowl.
From the graph’s intersection at the 10-minute mark:

Bowl A shows approximately 24 liters.
Bowl B shows approximately 64 liters.

We confirm these values against the provided answer options.

Thus, after 10 minutes of pumping water, Bowl A contains $24$ liters, and Bowl B contains $64$ liters.

Therefore, the solution to the problem is $A:24, B:64$ .

Final Answer

$A:24,B:64$

Key Points to Remember

Essential concepts to master this topic

Reading Graphs: Find intersection of time and water level lines
Technique: At 10 minutes, trace vertical line to each bowl's curve
Check: Bowl A starts at 0, Bowl B at 32 liters initially ✓

Common Mistakes

Avoid these frequent errors

Reading the wrong axis or mixing up the bowl labels
Don't read horizontally from the y-axis numbers to find time = wrong coordinates! This gives you water levels at wrong times or mixes up which bowl is which. Always trace vertically from the time axis up to each curve, then read horizontally to the water level axis.

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 tell which line represents which bowl?

Look at the starting points at time 0! Bowl A starts at 0 liters (bottom line), while Bowl B starts at 32 liters (upper line). The graph also labels them as A and B.

What if the lines don't pass exactly through grid points?

Estimate as closely as possible! Look at the nearest grid lines and interpolate between them. For this problem, the lines pass through clear points at 10 minutes.

Why does Bowl B start with water while Bowl A is empty?

This is given in the problem setup! Bowl A starts empty and Bowl B starts with 32 liters. Always read the initial conditions carefully.

Do both bowls fill at the same rate?

No! Look at the slopes of the lines. Bowl A fills faster (steeper line) while Bowl B fills slower (gentler slope). The rates are different for each bowl.

How can I double-check my answer?

Verify that your values make sense: Bowl A should increase from 0, Bowl B should increase from 32. Also check that your answers match one of the given multiple choice options.

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