Calculate Time to Reach 64 Liters: Two-Bowl Water Flow Graph Analysis

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

Look at the starting points! Bowl A starts empty (0 liters) and Bowl B starts with 32 liters. The line starting at 32 liters is Bowl B, which is what the question asks about.

Q: What if the intersection point isn't exactly on a grid line?

Use the closest grid lines to estimate. In this case, the intersection is exactly at the 10-minute mark on the time axis, making it easy to read.

Q: Why does Bowl B fill up slower than Bowl A?

Look at the slopes of the lines! Bowl A has a steeper slope, meaning it fills faster. Bowl B has a gentler slope because it's filling at a slower rate.

Q: What does the graph tell me about the filling rates?

The slope of each line shows the filling rate. Steeper slopes mean faster filling. You can calculate: Bowl A fills about 4.8 liters/minute, Bowl B fills about 3.2 liters/minute.

Graph Reading with Linear Water Flow

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 64 liters of water in the tank B?

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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 64 liters of water in the tank B?

Step-by-step solution

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

Step 1: Identify starting condition. Bowl B initially has 32 liters.
Step 2: Use the graph to track the line for bowl B. This line starts at the point (0, 32) on the graph.
Step 3: Locate the point where this line intersects with the horizontal line representing 64 liters.
Step 4: From this intersection point, read down to the time axis to find the corresponding time value.

From the graph, bowl B reaches 64 liters at t = 10 minutes.

Therefore, the correct number of minutes after the taps are opened for bowl B to contain 64 liters of water is 10 minutes.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Initial Conditions: Bowl B starts with 32 liters at time zero
Technique: Find where line B crosses 64-liter mark: at t = 10 minutes
Check: Verify by tracing from 64 liters horizontally to line B, then down to time axis ✓

Common Mistakes

Avoid these frequent errors

Reading the wrong line on the graph
Don't confuse line A with line B = wrong starting point and wrong answer! Line A starts at 0 liters while line B starts at 32 liters as stated in the problem. Always identify which bowl the question asks about and trace 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:

FAQ

Everything you need to know about this question

How do I tell which line represents which bowl?

Look at the starting points! Bowl A starts empty (0 liters) and Bowl B starts with 32 liters. The line starting at 32 liters is Bowl B, which is what the question asks about.

What if the intersection point isn't exactly on a grid line?

Use the closest grid lines to estimate. In this case, the intersection is exactly at the 10-minute mark on the time axis, making it easy to read.

Why does Bowl B fill up slower than Bowl A?

Look at the slopes of the lines! Bowl A has a steeper slope, meaning it fills faster. Bowl B has a gentler slope because it's filling at a slower rate.

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

Follow these steps: 1) Find 64 on the y-axis, 2) Draw a horizontal line to where it meets line B, 3) Draw a vertical line down to the x-axis, 4) Read the time value.

What does the graph tell me about the filling rates?

The slope of each line shows the filling rate. Steeper slopes mean faster filling. You can calculate: Bowl A fills about 4.8 liters/minute, Bowl B fills about 3.2 liters/minute.

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