A walks at a uniform speed of 8 km/hr and 8 hours after his start, B start on his cycle after him at the speed of 24 km/hr. How far (in km) from the starting point will B catch A?

Options

A. 72
B. 96
C. 120
D. 144

Answer

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

### Step 1: Calculate the distance A covers before B starts.
A walks at a speed of 8 km/hr. Since A starts 8 hours before B, we can calculate the distance A covers in that time.

Distance = Speed × Time
Distance_A = 8 km/hr × 8 hr = 64 km

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

### Step 2: Determine the relative speed of B with respect to A.
B cycles at a speed of 24 km/hr, while A walks at 8 km/hr. Since they are moving in the same direction, we find the relative speed by subtracting A's speed from B's speed.

Relative Speed = Speed_B - Speed_A
Relative Speed = 24 km/hr - 8 km/hr = 16 km/hr

**Hint:** When two objects move in the same direction, the relative speed is found by subtracting the slower speed from the faster speed.

### Step 3: Calculate the time it takes for B to catch A.
Now that we know the lead distance (64 km) and the relative speed (16 km/hr), we can find the time it takes for B to catch A using the formula:

Time = Distance / Relative Speed
Time = 64 km / 16 km/hr = 4 hours

**Hint:** To find the time taken to cover a certain distance at a specific speed, divide the distance by the speed.

### Step 4: Calculate the distance B travels in that time.
Now, we need to find out how far B travels in the 4 hours it takes to catch A. We can use B's speed for this calculation.

Distance_B = Speed_B × Time
Distance_B = 24 km/hr × 4 hr = 96 km

**Hint:** Use the same formula for distance to find out how far B travels in the time it takes to catch A.

### Step 5: Conclusion
B will catch A at a distance of 96 km from the starting point.

**Final Answer:** B catches A at a distance of **96 km** from the starting point.

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