A train when moves at an average speed of 40 kmph, reaches its destination. When its average speed becomes 35 kmph, then it reaches its destination 15 late. Find the distance of journey is:

Options

A. 30 km
B. 40 km
C. 70 km
D. 80 km

Answer

To solve the problem step by step, we will use the relationship between speed, time, and distance.

### Step 1: Understand the problem
We know that when the train travels at 40 km/h, it reaches its destination on time. However, when it travels at 35 km/h, it arrives 15 minutes late. We need to find the distance of the journey.

### Step 2: Define variables
Let the distance of the journey be \( D \) kilometers.

### Step 3: Calculate time taken at different speeds
- Time taken at 40 km/h:
\[ \text{Time} = \frac{D}{40} \text{ hours} \]

- Time taken at 35 km/h:
\[ \text{Time} = \frac{D}{35} \text{ hours} \]

### Step 4: Set up the equation for the time difference
According to the problem, the difference in time when the speed changes from 40 km/h to 35 km/h is 15 minutes. We need to convert 15 minutes into hours:
\[ 15 \text{ minutes} = \frac{15}{60} = \frac{1}{4} \text{ hours} \]

Now we can set up the equation:
\[ \frac{D}{35} - \frac{D}{40} = \frac{1}{4} \]

### Step 5: Solve the equation
To solve the equation, we need a common denominator for the fractions on the left side. The least common multiple of 35 and 40 is 280.

Rewriting the equation:
\[ \frac{8D}{280} - \frac{7D}{280} = \frac{1}{4} \]

This simplifies to:
\[ \frac{D}{280} = \frac{1}{4} \]

Now, cross-multiply to solve for \( D \):
\[ D = 280 \times \frac{1}{4} = 70 \text{ kilometers} \]

### Step 6: Conclusion
The distance of the journey is \( D = 70 \) kilometers.

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