Question

John jogs on track A at 6 kmph and Mary jogs on track B at 7.5 kmph. The total length of tracks A and B is 325 metres. While John makes 9 rounds of track A, Mary makes 5 rounds of track B. In how many seconds will Mary make one round of track A?

[TITA]

Accepted Answer

48. Speed of John $v_J = 6 	imes \frac{5}{18} = \frac{5}{3}	ext{ m/s}$. Speed of Mary $v_M = 7.5 	imes \frac{5}{18} = \frac{25}{12}	ext{ m/s}$. Let the lengths of tracks A and B be $L_A$ and $L_B$ respectively. $L_A + L_B = 325	ext{ m}$. 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 $L_A + L_B = 325$: $$L_A + \frac{9}{4} L_A = 325 \implies \frac{13}{4} L_A = 325 \implies L_A = 100	ext{ m}$$ Time taken by Mary to complete one round of track A: $$T = \frac{L_A}{v_M} = \frac{100}{25/12} = 48	ext{ seconds}$$

Jogging on tracks

Explanation

Practise this under exam conditions