Time Speed Distance problem 1 by Dhaval Furia

Algebra Level pending

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


The answer is 48.

Dhaval Furia by Dhaval Furia , 26, India

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1 solution

6 6 kmph = 5 3 \dfrac{5}{3} m/s. 7.5 7.5 kmph = 25 12 \dfrac{25}{12} m/s.

Let the length of track A A be l l . Then that of track B B is 325 − l 325-l . Time taken by John to make one round is 3 l 5 \dfrac{3l}{5} sec. and by Mary is 12 ( 325 − l ) 25 \dfrac{12(325-l)}{25} sec.

Therefore 9 × 3 l 5 = 5 × 12 ( 325 − l ) 25 ⟹ l = 100 9\times \dfrac{3l}{5}=5\times \dfrac{12(325-l)}{25}\implies l=100 .

Therefore time taken by Mary to make one round in track A A is 100 × 12 25 = 48 100\times \dfrac{12}{25}=\boxed {48} sec.

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