6. In an inter-school athletics track competition, each school team will consist of three athletes for the 100 m event, \( x \) athletes for the 200 m event, and \( y \) athletes for the 400 m event. Write down in terms of \( x \) and \( y \), an expression for (a) the number of track athletes in each school team, (b) the total distance, in kilometers, to be covered by the track athletes of each school team.

To solve the problem, we need to express the number of athletes in each school team and the total distance covered by these athletes in terms of \( x \) and \( y \). ### (a) Number of track athletes in each school team Each school team consists of: - 3 athletes for the 100 m event - \( x \) athletes for the 200 m event - \( y \) athletes for the 400 m event Thus, the total number of track athletes in each school team can be expressed as: \[ \text{Total number of athletes} = 3 + x + y \] ### (b) Total distance to be covered by the track athletes of each school team The distances covered by the athletes in each event are as follows: - Each of the 3 athletes in the 100 m event covers 100 m. - Each of the \( x \) athletes in the 200 m event covers 200 m. - Each of the \( y \) athletes in the 400 m event covers 400 m. Now, we can calculate the total distance covered by all athletes in each school team: 1. Distance covered by 100 m athletes: \[ 3 \times 100 \text{ m} = 300 \text{ m} \] 2. Distance covered by 200 m athletes: \[ x \times 200 \text{ m} = 200x \text{ m} \] 3. Distance covered by 400 m athletes: \[ y \times 400 \text{ m} = 400y \text{ m} \] Now, we can sum these distances to find the total distance covered by the track athletes: \[ \text{Total distance} = 300 \text{ m} + 200x \text{ m} + 400y \text{ m} \] To express this total distance in kilometers, we convert meters to kilometers (1 km = 1000 m): \[ \text{Total distance in kilometers} = \frac{300 + 200x + 400y}{1000} \] Thus, the final expressions are: (a) The number of track athletes in each school team: \[ 3 + x + y \] (b) The total distance to be covered by the track athletes of each school team (in kilometers): \[ \frac{300 + 200x + 400y}{1000} \]