Motor- cyclist P started his journey at a speed of 30km/hr. After 30 minutes , motor- cyclist Q started from the same place but with a speed of 40 km/hr. how much time (in hours) will Q take to overtake P?

Options

A. 1
B. `(3)/(2)`
C. `(3)/(8)`
D. 2

Answer

To solve the problem, we need to determine how long it will take for motor-cyclist Q to overtake motor-cyclist P after Q starts his journey.

### Step-by-Step Solution:

1. **Determine the distance covered by P in the first 30 minutes:**
- P's speed = 30 km/hr.
- Time = 30 minutes = 0.5 hours.
- Distance = Speed × Time = 30 km/hr × 0.5 hr = 15 km.
- So, after 30 minutes, P is 15 km ahead of the starting point.

**Hint:** Remember that distance is calculated by multiplying speed by time.

2. **Determine the relative speed of Q with respect to P:**
- Q's speed = 40 km/hr.
- P's speed = 30 km/hr.
- Relative speed = Q's speed - P's speed = 40 km/hr - 30 km/hr = 10 km/hr.

**Hint:** When two objects are moving in the same direction, the relative speed is the difference between their speeds.

3. **Calculate the time taken by Q to cover the distance of 15 km:**
- Distance to be covered by Q to overtake P = 15 km.
- Time = Distance / Relative Speed = 15 km / 10 km/hr = 1.5 hours.

**Hint:** Use the formula time = distance / speed to find how long it takes to cover a certain distance.

4. **Final Answer:**
- Q will take 1.5 hours to overtake P.

### Summary:
Motor-cyclist Q will take **1.5 hours** to overtake motor-cyclist P after starting his journey.