A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of `72 kmh^-1`. The jeep follows it at as peed of 108 kmh^-1`, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike.

Explanation

To solve the problem of how far from the turning the police jeep will catch up with the motorbike, we can break it down into a series of steps:

### Step 1: Convert the speeds from km/h to m/s
The speed of the motorbike is given as 72 km/h. To convert this to meters per second, we use the conversion factor \( \frac{5}{18} \):

\[ \text{Speed of bike} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

The speed of the police jeep is given as 108 km/h. We convert this similarly:

\[ \text{Speed of police} = 108 \times \frac{5}{18} = 30 \text{ m/s} \]

### Step 2: Determine the time difference in their departures
The police jeep starts chasing the motorbike 10 seconds after the motorbike has already crossed the turning point. During this time, the motorbike travels a certain distance.

### Step 3: Calculate the distance traveled by the motorbike in 10 seconds
Using the speed of the motorbike, we can find the distance it travels in those 10 seconds:

\[ \text{Distance traveled by bike} = \text{Speed} \times \text{Time} = 20 \text{ m/s} \times 10 \text{ s} = 200 \text{ m} \]

### Step 4: Set up the equations for the distances traveled
Let \( t \) be the time in seconds after the police jeep starts chasing. The distance traveled by the police jeep in time \( t \) is:

\[ \text{Distance traveled by police} = 30 \text{ m/s} \times t \]

The total distance traveled by the motorbike after the police jeep has started chasing is:

\[ \text{Distance traveled by bike} = 20 \text{ m/s} \times t + 200 \text{ m} \]

### Step 5: Set the distances equal to find \( t \)
At the point when the police jeep catches up with the motorbike, the distances will be equal:

\[ 30t = 20t + 200 \]

### Step 6: Solve for \( t \)
Rearranging the equation gives:

\[ 30t - 20t = 200 \\ 10t = 200 \\ t = 20 \text{ seconds} \]

### Step 7: Calculate the distance from the turning point where the jeep catches the bike
Now that we have the time \( t \) it takes for the police jeep to catch up after it starts chasing, we can find the distance traveled by the police jeep during this time:

\[ \text{Distance} = \text{Speed of police} \times \text{Time} = 30 \text{ m/s} \times 20 \text{ s} = 600 \text{ m} \]

Thus, the distance from the turning point where the police jeep catches up with the motorbike is **600 meters**.

### Summary of Steps:
1. Convert speeds from km/h to m/s.
2. Determine the time difference in their departures.
3. Calculate the distance traveled by the motorbike in the time difference.
4. Set up equations for the distances traveled by both vehicles.
5. Solve for the time \( t \) when the police jeep catches the motorbike.
6. Calculate the distance from the turning point.