A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h.
The jeep follows it at a speed of 90 km/h, 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 clear steps:

### Step 1: Convert Speeds from km/h to m/s
The speed of the motorbike is given as 72 km/h. We convert this to meters per second (m/s):
\[ \text{Speed of motorbike} = 72 \times \frac{1000}{3600} = 20 \text{ m/s} \]

The speed of the police jeep is given as 90 km/h. We convert this to meters per second (m/s):
\[ \text{Speed of police jeep} = 90 \times \frac{1000}{3600} = 25 \text{ m/s} \]

### Step 2: Calculate the Distance Covered by the Motorbike in 10 Seconds
The motorbike crosses the turning first and travels for 10 seconds before the jeep starts. The distance covered by the motorbike in this time is:
\[ \text{Distance covered by motorbike} = \text{Speed} \times \text{Time} = 20 \text{ m/s} \times 10 \text{ s} = 200 \text{ m} \]

### Step 3: Determine the Relative Speed Between the Jeep and the Motorbike
The relative speed of the jeep with respect to the motorbike is:
\[ \text{Relative speed} = \text{Speed of jeep} - \text{Speed of motorbike} = 25 \text{ m/s} - 20 \text{ m/s} = 5 \text{ m/s} \]

### Step 4: Calculate the Time Taken for the Jeep to Catch Up
Now, we need to find out how long it will take for the jeep to cover the 200 m distance that the motorbike has already traveled. Using the relative speed:
\[ \text{Time to catch up} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{200 \text{ m}}{5 \text{ m/s}} = 40 \text{ s} \]

### Step 5: Calculate the Distance Covered by the Jeep During This Time
Finally, we calculate the distance that the jeep covers in the time it takes to catch up:
\[ \text{Distance covered by jeep} = \text{Speed of jeep} \times \text{Time} = 25 \text{ m/s} \times 40 \text{ s} = 1000 \text{ m} \]

### Final Answer
Thus, the police jeep will catch up with the motorbike at a distance of **1000 meters (or 1 km)** from the turning.

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