Jacob and Sophia are in a running club and record how long it takes them to run a 5-kilometer race. Jacob's time was 4 minutes under the average time of the running club. The difference between Jacob's time and Sophia's time is 10 minutes.

Question

The possible times of Sophia's run are
minutes below the average or
minutes above the average.

Answer 1

Let \( A \) be the average time of the running club. Jacob's time \( J \) is then:

\[ J = A - 4 \]

Sophia's time \( S \) has a difference of 10 minutes from Jacob's time:

\[ |S - J| = 10 \]

This gives us two cases to consider:

1. \( S - J = 10 \)
2. \( J - S = 10 \)

Case 1: \( S - J = 10 \)

Substituting Jacob's time into this equation:

\[ S - (A - 4) = 10 \]

Rearranging this gives us:

\[ S = A - 4 + 10 \] \[ S = A + 6 \]

In this case, Sophia's time \( S \) is 6 minutes above the average.

Case 2: \( J - S = 10 \)

Substituting Jacob's time again:

\[ (A - 4) - S = 10 \]

Rearranging this gives:

\[ A - S - 4 = 10 \] \[ A - S = 14 \] \[ S = A - 14 \]

In this case, Sophia's time \( S \) is 14 minutes below the average.

Summary

Combining both cases, the possible times of Sophia’s run are:

• \( 14 \) minutes below the average (from Case 2)
• \( 6 \) minutes above the average (from Case 1)

Thus, the final answer is: 14 minutes below the average or 6 minutes above the average.