A certain jet plane has an average speed of 500 km per hour. It can carry sufficient fuel for a 5 hour flight.
Define the relation, as a set, between the distance d (in km) and time t (in hours) for this plane.

Answer

To define the relation between distance \( d \) (in kilometers) and time \( t \) (in hours) for the given jet plane, we can follow these steps:

### Step 1: Understand the relationship between distance, speed, and time.
The relationship is given by the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]
Given that the average speed of the jet plane is 500 km/h, we can express this as:
\[ 500 = \frac{d}{t} \]

### Step 2: Rearrange the formula to express distance in terms of time.
From the speed formula, we can rearrange it to find distance \( d \):
\[ d = 500t \]

### Step 3: Determine the constraints on time.
The plane can carry sufficient fuel for a 5-hour flight, which means the maximum time \( t \) is 5 hours. Therefore, \( t \) can take any value from 0 to 5 hours.

### Step 4: Define the relation as a set.
We can now define the relation \( R \) between distance \( d \) and time \( t \) in set builder notation. The relation can be expressed as:
\[ R = \{ (d, t) \mid d = 500t, \, t \in [0, 5] \} \]

### Final Relation:
Thus, the relation between distance \( d \) and time \( t \) for the plane can be summarized as:
\[ R = \{ (d, t) \mid d = 500t, \, 0 \leq t \leq 5 \} \]

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