A police is chasing a culprit going n 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 tenseconds latert than the bike. Assuming that they tavel at constant speeds, how far from the turning will the jeep catch up with the bike?

Explanation

To solve the problem, we need to determine how far from the turning the police jeep will catch up with the motorbike. We will follow these steps:

### Step 1: Convert Speeds from km/h to m/s
The speeds of both the motorbike and the jeep are given in kilometers per hour (km/h). We need to convert these speeds to meters per second (m/s) for easier calculations.

- Speed of the motorbike = 72 km/h
\[ \text{Speed in m/s} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

- Speed of the jeep = 90 km/h
\[ \text{Speed in m/s} = 90 \times \frac{5}{18} = 25 \text{ m/s} \]

### Step 2: Calculate the Distance Covered by the Motorbike in 10 Seconds
The motorbike crosses the turning 10 seconds before the jeep starts chasing. We need to find out how far the motorbike travels in those 10 seconds.

- Distance covered by the motorbike in 10 seconds:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ m/s} \times 10 \text{ s} = 200 \text{ meters} \]

### Step 3: Determine the Relative Speed of the Jeep with Respect to the Motorbike
Since both vehicles are moving in the same direction, we can find the relative speed by subtracting the speed of the motorbike from the speed of the jeep.

- Relative speed:
\[ \text{Relative Speed} = \text{Speed of Jeep} - \text{Speed of Motorbike} = 25 \text{ m/s} - 20 \text{ m/s} = 5 \text{ m/s} \]

### Step 4: Calculate the Time Taken for the Jeep to Catch Up
Now, we need to determine how long it will take for the jeep to cover the distance of 200 meters that the motorbike has already traveled.

- Time taken to catch up:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} = \frac{200 \text{ meters}}{5 \text{ m/s}} = 40 \text{ seconds} \]

### Step 5: Calculate the Distance the Jeep Travels in 40 Seconds
Now that we know it takes 40 seconds for the jeep to catch up, we can calculate how far the jeep travels in that time.

- Distance traveled by the jeep:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 25 \text{ m/s} \times 40 \text{ s} = 1000 \text{ meters} \]

### Conclusion
The jeep will catch up with the motorbike 1000 meters from the turning point.

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