An express train travelled at an average speed of 100 `"km"//"hr"`, stopping for 3 minutes after every 75 km. How long it take to reach its destination 600 km from the starting point ?

Options

A. 6 hrs 21 min
B. 6 hrs 24 min
C. 6 hrs 27 min
D. 6 hrs 30 min

Answer

To solve the problem step by step, we will calculate the total time taken by the express train to travel 600 km, including the time taken for stops.

### Step 1: Calculate the time taken to travel 600 km without stops.
- **Formula**: Time = Distance / Speed
- **Distance** = 600 km
- **Speed** = 100 km/h

**Calculation**:
\[ \text{Time} = \frac{600 \text{ km}}{100 \text{ km/h}} = 6 \text{ hours} \]

### Step 2: Determine how many stops the train makes.
- The train stops every 75 km.
- **Total distance** = 600 km
- **Distance per stop** = 75 km

**Calculation**:
\[ \text{Number of stops} = \frac{600 \text{ km}}{75 \text{ km}} - 1 = 8 - 1 = 7 \text{ stops} \]
(Note: We subtract 1 because the train does not stop after reaching the destination.)

### Step 3: Calculate the total stopping time.
- **Time per stop** = 3 minutes
- **Number of stops** = 7

**Calculation**:
\[ \text{Total stopping time} = 7 \text{ stops} \times 3 \text{ minutes/stop} = 21 \text{ minutes} \]

### Step 4: Convert the total time into hours and minutes.
- **Total travel time** = 6 hours
- **Total stopping time** = 21 minutes

**Final Calculation**:
The total time taken to reach the destination is:
\[ \text{Total time} = 6 \text{ hours} + 21 \text{ minutes} \]

### Final Answer:
The express train takes **6 hours and 21 minutes** to reach its destination.

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