Jogging on tracks

Speed of John $v_J = 6 \times \frac{5}{18} = \frac{5}{3}\text{ m/s}$. Speed of Mary $v_M = 7.5 \times \frac{5}{18} = \frac{25}{12}\text{ m/s}$.

Let the lengths of tracks A and B be $L_A$ and $L_B$ respectively. $L_A + L_B = 325\text{ m}$.

Time taken by John for 9 rounds of track A = Time taken by Mary for 5 rounds of track B: $\frac{9 L_A}{5/3} = \frac{5 L_B}{25/12}$ $\frac{27 L_A}{5} = \frac{12 L_B}{5} \implies 27 L_A = 12 L_B \implies L_B = \frac{9}{4} L_A$

Substitute into $L_A + L_B = 325$: $L_A + \frac{9}{4} L_A = 325 \implies \frac{13}{4} L_A = 325 \implies L_A = 100\text{ m}$

Time taken by Mary to complete one round of track A: $T = \frac{L_A}{v_M} = \frac{100}{25/12} = 48\text{ seconds}$