A person leaves Hyderabad at 7 : 00 a.m. and reaches Chennai, which is at a distance of 360 km at 1:00 p.m. After taking half -an - hour rest, he again leaves Chennai and reaches Hyderabad at 9:00 p.m. Find the decrease in his speed while coming back to Hyderabad, If he maintains uniform speed .

Answer

To solve the problem step by step, we will calculate the speed of the person while traveling from Hyderabad to Chennai and then from Chennai back to Hyderabad. Finally, we will find the decrease in speed.

### Step 1: Calculate the time taken to travel from Hyderabad to Chennai.

The person leaves Hyderabad at 7:00 a.m. and reaches Chennai at 1:00 p.m.

- **Time taken** = 1:00 p.m. - 7:00 a.m. = 6 hours

### Step 2: Calculate the speed from Hyderabad to Chennai.

The distance from Hyderabad to Chennai is 360 km.

- **Speed** = Distance / Time
- Speed = 360 km / 6 hours = 60 km/h

### Step 3: Calculate the time taken to travel back from Chennai to Hyderabad.

The person leaves Chennai after a half-hour rest at 1:00 p.m., which means he starts at 1:30 p.m. and reaches Hyderabad at 9:00 p.m.

- **Time taken** = 9:00 p.m. - 1:30 p.m. = 7.5 hours

### Step 4: Calculate the speed from Chennai to Hyderabad.

- **Speed** = Distance / Time
- Speed = 360 km / 7.5 hours = 48 km/h

### Step 5: Calculate the decrease in speed.

- Decrease in speed = Speed from Hyderabad to Chennai - Speed from Chennai to Hyderabad
- Decrease in speed = 60 km/h - 48 km/h = 12 km/h

### Final Answer:
The decrease in speed while coming back to Hyderabad is **12 km/h**.

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