A police is chasing a culprit going in 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 10 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, we will follow these steps:

### Step 1: Convert the speeds from km/h to m/s
The speeds of the motorbike and the jeep are given in km/h. We need to convert these speeds to m/s for easier calculations.

- Speed of the motorbike = 72 km/h = \( \frac{72 \times 1000}{3600} = 20 \) m/s
- Speed of the jeep = 90 km/h = \( \frac{90 \times 1000}{3600} = 25 \) m/s

### Step 2: Calculate the distance the motorbike travels in 10 seconds
Since the jeep starts chasing the motorbike 10 seconds after it has crossed the turning, we need to find out how far the motorbike travels in those 10 seconds.

- Distance traveled by the motorbike in 10 seconds = Speed × Time
- Distance = \( 20 \, \text{m/s} \times 10 \, \text{s} = 200 \, \text{m} \)

### Step 3: Determine the relative speed of the jeep with respect to the motorbike
Now, we need to find the relative speed between the jeep and the motorbike to determine how quickly the jeep is catching up.

- Relative speed = Speed of jeep - Speed of motorbike
- Relative speed = \( 25 \, \text{m/s} - 20 \, \text{m/s} = 5 \, \text{m/s} \)

### Step 4: Calculate the time taken by the jeep to catch up with the motorbike
The jeep needs to cover the distance that the motorbike has already traveled in the 10 seconds, which is 200 m. We can find the time taken to catch up using the formula:

- Time = Distance / Relative Speed
- Time = \( \frac{200 \, \text{m}}{5 \, \text{m/s}} = 40 \, \text{s} \)

### Step 5: Calculate the distance from the turning point where the jeep catches the motorbike
Now that we know the time taken by the jeep to catch up with the motorbike, we can find out how far the jeep travels from the turning point during this time.

- Distance = Speed × Time
- Distance traveled by the jeep = \( 25 \, \text{m/s} \times 40 \, \text{s} = 1000 \, \text{m} \)

Thus, the jeep will catch up with the motorbike **1000 meters** from the turning point.

### Final Answer:
The jeep will catch up with the bike at a distance of **1000 meters** from the turning point.

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