A walks at a uniform rate of 4 km an hour and 4 hours after his start, B bicycles after him at the uniform rate of 10 km an hours. How far from the starting point will B catch A?

Options

A. 16.7km
B. 18.6km
C. 21.5km
D. 26.7km

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Calculate the distance A travels in 4 hours.
- A walks at a speed of 4 km/h.
- Time taken by A before B starts is 4 hours.

**Distance = Speed × Time**
- Distance traveled by A = 4 km/h × 4 hours = 16 km.

### Step 2: Determine the relative speed of B with respect to A.
- A's speed = 4 km/h
- B's speed = 10 km/h

**Relative Speed = Speed of B - Speed of A**
- Relative Speed = 10 km/h - 4 km/h = 6 km/h.

### Step 3: Calculate the time it takes for B to catch A.
- The distance between A and B when B starts is 16 km (the distance A has already covered).

**Using the formula: Time = Distance / Speed**
- Time taken for B to catch A = Distance / Relative Speed = 16 km / 6 km/h = 16/6 hours = 8/3 hours.

### Step 4: Calculate the distance B travels during this time.
- B's speed = 10 km/h.
- Time taken = 8/3 hours.

**Distance = Speed × Time**
- Distance traveled by B = 10 km/h × (8/3) hours = 80/3 km.

### Step 5: Calculate the total distance from the starting point.
- Since B starts from the starting point, the distance B travels to catch A is the distance from the starting point.

**Distance from starting point = 80/3 km ≈ 26.67 km.**

### Final Answer:
B will catch A approximately **26.67 km** from the starting point.

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