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:
- \( S - J = 10 \)
- \( J - S = 10 \)
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.