A person drives his car for 3 hours at a speed of 40 km/hr and for 4.5 hour at a speed of 60 km/hr. At the end of it he find that he has covered ` (3)/(5)` of the total distance. What is the uniform speed with which he should further drive to cover the remaining distance in 4 hours?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the distance covered in the first part of the journey.

The person drives for:
- 3 hours at a speed of 40 km/hr
- 4.5 hours at a speed of 60 km/hr

**Distance covered in the first part:**
1. Distance for the first part = Speed × Time = 40 km/hr × 3 hours = 120 km
2. Distance for the second part = Speed × Time = 60 km/hr × 4.5 hours = 270 km

**Total distance covered in the first part:**
\[ \text{Total Distance} = 120 \text{ km} + 270 \text{ km} = 390 \text{ km} \]

### Step 2: Determine the total distance.

According to the problem, the distance covered (390 km) is \( \frac{3}{5} \) of the total distance (let's denote the total distance as \( D \)).

So, we can set up the equation:
\[ \frac{3}{5}D = 390 \text{ km} \]

### Step 3: Solve for the total distance \( D \).

To find \( D \), we can rearrange the equation:
\[ D = 390 \text{ km} \times \frac{5}{3} \]
\[ D = 650 \text{ km} \]

### Step 4: Calculate the remaining distance.

The remaining distance to be covered is:
\[ \text{Remaining Distance} = D - \text{Distance Covered} \]
\[ \text{Remaining Distance} = 650 \text{ km} - 390 \text{ km} = 260 \text{ km} \]

### Step 5: Determine the speed needed to cover the remaining distance in 4 hours.

Let \( v \) be the uniform speed required. We know that:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Thus,
\[ 260 \text{ km} = v \times 4 \text{ hours} \]

### Step 6: Solve for \( v \).

Rearranging the equation gives:
\[ v = \frac{260 \text{ km}}{4 \text{ hours}} \]
\[ v = 65 \text{ km/hr} \]

### Final Answer:
The uniform speed with which he should further drive to cover the remaining distance in 4 hours is **65 km/hr**.

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