An express train travelled at an average speed of100km/h ,stopping for 3 min after every 75 km.A local train travelled data speed of 50km/h ,stopping for 1 min after every 25km. If the trains began travelling at the same time, how many kilometres did the local train travel in the time in which the express train travel 600 km?

Options

A. 400 km
B. 405 km
C. 307.25 km
D. 415.5 km

Answer

To solve the problem, we need to calculate the total time taken by the express train to travel 600 km, including the time spent stopping, and then determine how far the local train travels in that same time.

### Step 1: Calculate the time taken by the express train to travel 600 km without stops.
The express train travels at a speed of 100 km/h.

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{600 \text{ km}}{100 \text{ km/h}} = 6 \text{ hours} \]

**Hint:** To find the time taken to travel a distance at a constant speed, use the formula: Time = Distance / Speed.

### Step 2: Determine how many stops the express train makes.
The express train stops for 3 minutes after every 75 km.

To find out how many 75 km segments are in 600 km:

\[ \text{Number of segments} = \frac{600 \text{ km}}{75 \text{ km}} = 8 \]

Since the train only stops after completing each segment, it will stop 7 times (after the first 7 segments).

**Hint:** Remember that the number of stops is always one less than the number of segments traveled.

### Step 3: Calculate the total stopping time for the express train.
Each stop lasts 3 minutes, and there are 7 stops:

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

**Hint:** To find total stopping time, multiply the number of stops by the duration of each stop.

### Step 4: Convert the total time taken by the express train into hours.
The total time taken by the express train is:

\[ \text{Total time} = 6 \text{ hours} + 21 \text{ minutes} \]

Convert 21 minutes into hours:

\[ 21 \text{ minutes} = \frac{21}{60} \text{ hours} = 0.35 \text{ hours} \]

So, the total time in hours is:

\[ \text{Total time} = 6 + 0.35 = 6.35 \text{ hours} \]

**Hint:** To convert minutes into hours, divide the number of minutes by 60.

### Step 5: Calculate the distance traveled by the local train in the same time.
The local train travels at a speed of 50 km/h. We need to find the distance it covers in 6.35 hours.

Using the formula for distance:

\[ \text{Distance} = \text{Speed} \times \text{Time} = 50 \text{ km/h} \times 6.35 \text{ hours} = 317.5 \text{ km} \]

**Hint:** To find the distance traveled, multiply the speed of the train by the time it travels.

### Final Answer:
The local train travels **317.5 km** in the time the express train travels 600 km.