Joyce and Felix tested their reaction times. Each person pressed a button as soon as a light turns on. They compared their reaction times with the average, represented by the zero mark on the number line. Joyce's reaction time was 0.1 seconds below the average reaction time. The difference between Joyce's reaction time and Felix's reaction time was 0.3 seconds. Plot all of the points on the number line that could represent Felix's reaction time as compared to the average.

Answer 1

To plot Joyce's and Felix's reaction times on a number line as compared to the average (0 mark), we can represent their reaction times as follows:

1. Joyce's Reaction Time:

   • Since Joyce's reaction time is 0.1 seconds below the average, we can denote it as: \[ J = -0.1 \text{ seconds} \]

2. Difference Between Joyce's and Felix's Reaction Times:

   • We know the difference between Joyce's and Felix's reaction times is 0.3 seconds. This means: \[ |J - F| = 0.3 \text{ seconds} \]
   • Since Joyce's reaction time \( J \) is -0.1, we can express Felix's reaction time \( F \) in two cases:
     • Case 1: Felix's reaction time is 0.3 seconds greater than Joyce's: \[ F = J + 0.3 = -0.1 + 0.3 = 0.2 \text{ seconds} \]
     • Case 2: Felix's reaction time is 0.3 seconds less than Joyce's: \[ F = J - 0.3 = -0.1 - 0.3 = -0.4 \text{ seconds} \]

3. Possible Values of Felix's Reaction Time:

   • Thus, Felix's reaction time could be \( F = 0.2 \) seconds or \( F = -0.4 \) seconds.

On a number line, we can mark the following points:

• The average (0 mark)
• Joyce's reaction time at \(-0.1\) seconds
• Felix's possible reaction times:
  • \(0.2\) seconds (above average)
  • \(-0.4\) seconds (below average)

Summary of Points to Plot:

• 0 (average)
• -0.1 (Joyce's reaction time)
• 0.2 (Felix's higher reaction time)
• -0.4 (Felix's lower reaction time)

You can visualize this on a number line with the mentioned points marked accordingly.