Amit walks at a uniform speed of 4 km/h and 4 h after his start, Brijesh cycles after him at the uniform rate of 20 km/h. How far from the starting point will Brijesh catch Amit?

Options

A. 15km
B. 18km
C. 13km
D. 20km

Answer

To solve the problem, we will break it down step by step.

### Step 1: Calculate the distance Amit covers before Brijesh starts cycling.
Amit walks at a speed of 4 km/h. He starts walking 4 hours before Brijesh starts cycling.

- Distance covered by Amit in 4 hours = Speed × Time
- Distance = 4 km/h × 4 h = 16 km

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

### Step 2: Determine the relative speed between Brijesh and Amit.
Brijesh cycles at a speed of 20 km/h, while Amit walks at a speed of 4 km/h. Since they are moving in the same direction, we find the relative speed by subtracting Amit's speed from Brijesh's speed.

- Relative speed = Speed of Brijesh - Speed of Amit
- Relative speed = 20 km/h - 4 km/h = 16 km/h

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

### Step 3: Calculate the time it takes for Brijesh to catch up with Amit.
Now, we know that Amit is 16 km ahead when Brijesh starts cycling. We need to find out how long it will take Brijesh to cover this distance at the relative speed we just calculated.

- Time = Distance / Relative Speed
- Time = 16 km / 16 km/h = 1 hour

**Hint:** Time can be calculated by dividing distance by speed.

### Step 4: Calculate the distance Brijesh travels in that time.
Now that we know it takes Brijesh 1 hour to catch Amit, we can find out how far Brijesh travels in that time.

- Distance traveled by Brijesh = Speed × Time
- Distance = 20 km/h × 1 h = 20 km

**Hint:** Again, use the formula for distance: Distance = Speed × Time.

### Conclusion
Brijesh will catch Amit 20 km away from the starting point.

**Final Answer:** Brijesh catches Amit 20 km from the starting point.

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