Time-Distance Graph: Finding Break Points for Two Cyclists Starting at 4 and 5

Distance-Time Graph Interpretation with Horizontal Segments

Two cyclists go out for a ride.

The first one starts at 4, while the second starts at 5.

At what times do the riders take a break?

Time000111222333444555666777888999101010111111121212131313141414151515161616555101010151515202020252525303030353535404040454545111222

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Step-by-step written solution

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1

Understand the problem

Two cyclists go out for a ride.

The first one starts at 4, while the second starts at 5.

At what times do the riders take a break?

Time000111222333444555666777888999101010111111121212131313141414151515161616555101010151515202020252525303030353535404040454545111222

2

Step-by-step solution

The graph suggests that Cyclist 1 takes a break starting at 6 o'clock, as indicated by the appearance of the red flat section starting at the marker for 6. Similarly, Cyclist 2 takes a break starting at 8 o'clock, identified from the blue flat section starting at the marker for 8.

Thus, the riders take their breaks at:

  • Cyclist 1 - at 6
  • Cyclist 2 - at 8

Therefore, the solution to the problem matches the given correct answer.

Conclusion: Cyclist 1 takes a break at t=6 t = 6 , and Cyclist 2 takes a break at t=8 t = 8 .

3

Final Answer

Cyclist 1 - at 6
Cyclist 2 - at 8

Key Points to Remember

Essential concepts to master this topic
  • Break Identification: Horizontal line segments indicate zero velocity (break periods)
  • Reading Technique: Find where line becomes flat, then read time on x-axis below
  • Verification: Cyclist 1 flat at t=6 t = 6 , Cyclist 2 flat at t=8 t = 8 āœ“

Common Mistakes

Avoid these frequent errors
  • Confusing break start times with distance values
    Don't read the distance (y-axis) values when asked for break times = wrong units! The distance tells you position, not when breaks occur. Always read the time values on the x-axis where horizontal segments begin.

Practice Quiz

Test your knowledge with interactive questions

Look at the function shown in the figure.

When is the function positive?

xy-4-7

FAQ

Everything you need to know about this question

How can I tell when a cyclist is taking a break?

+

Look for horizontal line segments on the graph! When the line is flat (not going up or down), it means the cyclist isn't moving - they're taking a break.

What's the difference between the red and blue lines?

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The red line represents Cyclist 1 (who started at position 4) and the blue line represents Cyclist 2 (who started at position 5). Each cyclist has their own separate journey.

Why do the cyclists start at different positions?

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This is common in real-world scenarios! Cyclists might start from different locations along a route. The starting positions are shown on the distance axis at time zero.

Can I determine how long each break lasted?

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Yes! Measure the length of each horizontal segment on the time axis. The longer the flat section, the longer the break period.

What if the graph shows multiple horizontal segments?

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Each horizontal segment represents a separate break. Read the time value where each flat section begins to find when each break started.

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