Ajay starts from his house to his office by his car which is 15 km away at an average speed of 45 km per hour. On the way back, he takes a route longer by 5 km since there is heavy traffic on the regular route. If he reaches home in the same time as the time he took to reach office in the morning, find his speed on the return journey.

Answer

To solve the problem step by step, we will first calculate the time taken by Ajay to reach his office and then use that to find his speed on the return journey.

### Step 1: Calculate the time taken to reach the office
Ajay travels a distance of 15 km to reach his office at an average speed of 45 km/h.

**Formula:**
Time = Distance / Speed

**Calculation:**
Time taken to reach the office = 15 km / 45 km/h
= 1/3 hours
= 20 minutes

### Step 2: Determine the distance on the return journey
On the way back, Ajay takes a longer route which is 5 km more than the distance to his office.

**Calculation:**
Distance on the return journey = 15 km + 5 km = 20 km

### Step 3: Set up the equation for speed on the return journey
Let the speed on the return journey be \( x \) km/h. Since he takes the same time to return as he did to go to the office, we can set up the equation using the time formula.

**Formula:**
Time = Distance / Speed

For the return journey:
Time taken = Distance on return / Speed on return
= 20 km / \( x \) km/h

### Step 4: Set the times equal
Since the time taken to go to the office is equal to the time taken to return home, we can set the two times equal to each other.

**Equation:**
1/3 hours = 20 km / \( x \) km/h

### Step 5: Solve for \( x \)
To solve for \( x \), we can cross-multiply:

**Calculation:**
1/3 = 20/x
=> 1 * x = 20 * 3
=> x = 60 km/h

### Conclusion
Ajay's speed on the return journey is **60 km/h**.

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