Kishlay travelled equal distances a speeds of 10 km/hr, 30km/hr,and 2 km/hr and took a total time of 38 minutes. Find the total distance in km.

Options

A. 2
B. 3
C. 1
D. 4

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Define the distance traveled
Let the distance traveled in each case be \( x \) km. Since Kishlay traveled equal distances at three different speeds, we will calculate the time taken for each segment of the journey.

### Step 2: Calculate the time taken for each speed
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
We can find the time taken for each speed:
- For the speed of 10 km/hr:
\[ \text{Time}_1 = \frac{x}{10} \text{ hours} \]
- For the speed of 30 km/hr:
\[ \text{Time}_2 = \frac{x}{30} \text{ hours} \]
- For the speed of 2 km/hr:
\[ \text{Time}_3 = \frac{x}{2} \text{ hours} \]

### Step 3: Set up the equation for total time
The total time taken for the journey is given as 38 minutes. We need to convert this into hours:
\[ 38 \text{ minutes} = \frac{38}{60} \text{ hours} \]
Now, we can set up the equation:
\[ \frac{x}{10} + \frac{x}{30} + \frac{x}{2} = \frac{38}{60} \]

### Step 4: Find a common denominator
The least common multiple (LCM) of the denominators (10, 30, and 2) is 30. Rewriting each term with a common denominator:
\[ \frac{3x}{30} + \frac{x}{30} + \frac{15x}{30} = \frac{38}{60} \]
Combining the left side:
\[ \frac{3x + x + 15x}{30} = \frac{38}{60} \]
This simplifies to:
\[ \frac{19x}{30} = \frac{38}{60} \]

### Step 5: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 19x \cdot 60 = 38 \cdot 30 \]
Calculating the right side:
\[ 19x \cdot 60 = 1140 \]
Now, divide both sides by 19:
\[ x \cdot 60 = \frac{1140}{19} \]
Calculating \( \frac{1140}{19} \):
\[ x \cdot 60 = 60 \quad \Rightarrow \quad x = 1 \]

### Step 6: Calculate the total distance
Since Kishlay traveled equal distances of \( x \) km in three segments, the total distance \( D \) is:
\[ D = x + x + x = 3x = 3 \times 1 = 3 \text{ km} \]

### Final Answer
The total distance traveled by Kishlay is **3 km**.

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