Question - Motion Around a Circular Track

Let the circular track be of circumference C. Tom completes 10 rounds, which means he covers a distance of 10C.

Laura completes 8 rounds, which means she covers a distance of 8C.

The speeds of Tom and Laura can be represented as:

Speed of Tom = 10C/t

Speed of Laura = 8C/t

In order to find how many complete rounds Laura makes before Tom reaches her, we can set up the equation:

Speed of Tom = Speed of Laura + distance covered by Laura in time t.

Let x be the number of complete rounds Laura runs before Tom catches up with her, which can be expressed as:

10C/t = 8C/t + (xC/t).

Solving for x:

10 = 8 + x,

x = 2.

Thus, Laura will have completed 2 complete rounds before Tom reaches her for the first time.