First, let's find the length of track A and track B.

We know that the total length of tracks A and B is 325 metres. We also know that while John makes 9 rounds of track A, Mary makes 5 rounds of track B.

So, we can set up the equation: 9A + 5B = 325

We also know that John jogs at 6 kmph and Mary jogs at 7.5 kmph. This means that the ratio of the length of track A to track B is the inverse of the ratio of their speeds.

So, A/B = 7.5/6 = 1.25

We can set up the equation: A = 1.25B

Now we can solve these two equations simultaneously to find the lengths of tracks A and B.

Substituting A = 1.25B into the first equation gives: 9(1.25B) + 5B = 325

This simplifies to: 11.25B + 5B = 325

And further simplifies to: 16.25B = 325

So, B = 325 / 16.25 = 20 metres

Substituting B = 20 into the equation A = 1.25B gives: A = 1.25 * 20 = 25 metres

Now we know that track A is 25 metres long.

We also know that Mary jogs at 7.5 kmph. To find out how long it takes her to jog one round of track A, we need to convert her speed to metres per second.

1 kmph = 1000 metres / 3600 seconds = 0.27778 metres per second

So, Mary jogs at 7.5 * 0.27778 = 2.08335 metres per second

Finally, to find out how long it takes her to jog one round of track A, we divide the length of track A by her speed.

So, it takes her 25 / 2.08335 = 12 seconds to jog one round of track A.

So, the answer is 12 seconds.

Question

First, let's find the length of track A and track B.

We know that the total length of tracks A and B is 325 metres. We also know that while John makes 9 rounds of track A, Mary makes 5 rounds of track B.

So, we can set up the equation: 9A + 5B = 325

We also know that John jogs at 6 kmph and Mary jogs at 7.5 kmph. This means that the ratio of the length of track A to track B is the inverse of the ratio of their speeds.

So, A/B = 7.5/6 = 1.25

We can set up the equation: A = 1.25B

Now we can solve these two equations simultaneously to find the lengths of tracks A and B.

Substituting A = 1.25B into the first equation gives: 9(1.25B) + 5B = 325

This simplifies to: 11.25B + 5B = 325

And further simplifies to: 16.25B = 325

So, B = 325 / 16.25 = 20 metres

Substituting B = 20 into the equation A = 1.25B gives: A = 1.25 * 20 = 25 metres

Now we know that track A is 25 metres long.

We also know that Mary jogs at 7.5 kmph. To find out how long it takes her to jog one round of track A, we need to convert her speed to metres per second.

1 kmph = 1000 metres / 3600 seconds = 0.27778 metres per second

So, Mary jogs at 7.5 * 0.27778 = 2.08335 metres per second

Finally, to find out how long it takes her to jog one round of track A, we divide the length of track A by her speed.

So, it takes her 25 / 2.08335 = 12 seconds to jog one round of track A.

So, the answer is 12 seconds.

Knowee AI · Accepted Answer