Renu travelled a certain distance in 2 hours and 5 minutes. She travelled this distance partly by car and partly by bus. The speed of the bus is 28 kmph and the speed of the car is 42 kmph. If the distance travelled by car is equal to the distance travelled by bus, what is the total distance that she travelled ?

Options

A. 70
B. 25
C. 40
D. 50

Answer

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

### Step 1: Understand the Problem
Renu travels a certain distance in 2 hours and 5 minutes, partly by car and partly by bus. The speeds of the bus and car are given, and the distances traveled by both are equal.

### Step 2: Convert Time into Hours
Convert the total time traveled from hours and minutes into hours:
- 2 hours and 5 minutes = 2 + (5/60) hours = 2 + 1/12 hours = 25/12 hours.

### Step 3: Define Variables
Let the distance traveled by car be \( D \) km. Since the distance traveled by bus is equal to the distance traveled by car, the distance traveled by bus is also \( D \) km.

### Step 4: Write the Time Equations
Using the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
We can write the time taken for each part of the journey:
- Time taken by bus = \( \frac{D}{28} \) hours
- Time taken by car = \( \frac{D}{42} \) hours

### Step 5: Set Up the Total Time Equation
The total time taken for the journey is the sum of the time taken by the bus and the car:
\[ \frac{D}{28} + \frac{D}{42} = \frac{25}{12} \]

### Step 6: Find a Common Denominator
To solve the equation, find a common denominator for the fractions on the left side. The least common multiple of 28 and 42 is 84:
\[ \frac{3D}{84} + \frac{2D}{84} = \frac{25}{12} \]
This simplifies to:
\[ \frac{5D}{84} = \frac{25}{12} \]

### Step 7: Cross Multiply to Solve for D
Cross-multiply to eliminate the fractions:
\[ 5D \cdot 12 = 25 \cdot 84 \]
This gives:
\[ 60D = 2100 \]

### Step 8: Solve for D
Now, divide both sides by 60:
\[ D = \frac{2100}{60} = 35 \text{ km} \]

### Step 9: Calculate Total Distance
Since the total distance traveled is \( 2D \):
\[ \text{Total Distance} = 2 \times 35 = 70 \text{ km} \]

### Final Answer
The total distance that Renu traveled is **70 km**.

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