In a race around a circular cycling track of 75 km, two cyclists are riding at a speed of 30 km/h and 25 km/h. After what time (in hours) will they meet at the point from where they started their journey?

To find the time at which the two cyclists meet at the starting point, we can use the concept of relative speed.

1. Speed of Cyclist A (faster cyclist): 30 km/h
2. Speed of Cyclist B (slower cyclist): 25 km/h
3. Relative Speed: The difference in their speeds is 30 km/h – 25 km/h = 5 km/h.

They will meet at the starting point when the faster cyclist covers a distance that is a multiple of the circular track’s circumference, in this case, 75 km.

To find the time it takes for the faster cyclist to cover the track’s distance:

– Time = Distance / Speed

Considering the complete lap required to meet at the starting point:

– Time for Cyclist A to complete one lap: ( frac{75 text{ km}}{30 text{ km/h}} = 2.5 text{ hours} )

– Time for Cyclist B to complete one lap: ( frac{75 text{ km}}{25 text{ km/h}} = 3 text{ hours} )

Now, we look for the least common multiple (LCM) of their times to determine when they will both be back at the starting point:

– LCM of 2.5 hours and 3 hours can be calculated as follows:

– Convert to fraction: 2.5 = (