A man travels some distance at a speed of 12km/hr and returns at a speed of 9km/hr. If the total time taken by him is 2 hrs 20 minutes the distance is

Options

A. 35km
B. 21km
C. 9km
D. 12km

Answer

To solve the problem, we need to find the distance traveled by the man. We know the speeds for both parts of the journey and the total time taken. Let's break it down step by step.

### Step 1: Convert the total time into hours
The total time given is 2 hours and 20 minutes. We need to convert this into hours.

\[ \text{Total time in hours} = 2 + \frac{20}{60} = 2 + \frac{1}{3} = \frac{7}{3} \text{ hours} \]

**Hint:** Remember that 20 minutes is \(\frac{1}{3}\) of an hour since there are 60 minutes in an hour.

### Step 2: Let the distance be \(d\) km
Let the distance traveled one way be \(d\) km.

### Step 3: Calculate the time taken for each part of the journey
The time taken to travel to the destination at 12 km/hr is:

\[ \text{Time}_{\text{to}} = \frac{d}{12} \text{ hours} \]

The time taken to return at 9 km/hr is:

\[ \text{Time}_{\text{return}} = \frac{d}{9} \text{ hours} \]

### Step 4: Set up the equation for total time
The total time for the journey is the sum of the time taken to go and return:

\[ \frac{d}{12} + \frac{d}{9} = \frac{7}{3} \]

**Hint:** Make sure to combine the fractions correctly. You will need a common denominator.

### Step 5: Find a common denominator
The least common multiple of 12 and 9 is 36. We can rewrite the equation:

\[ \frac{3d}{36} + \frac{4d}{36} = \frac{7}{3} \]

Combining the fractions gives:

\[ \frac{7d}{36} = \frac{7}{3} \]

### Step 6: Solve for \(d\)
To eliminate the fraction, multiply both sides by 36:

\[ 7d = 36 \times \frac{7}{3} \]

Calculating the right side:

\[ 7d = 12 \times 7 = 84 \]

Now, divide both sides by 7:

\[ d = \frac{84}{7} = 12 \text{ km} \]

### Final Answer
The distance is \(12\) km.

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