The distance between two places A and B is 245 km. Two cars, one from A and the other from B, start at the same time, travelling towards each other. If one car travels at a speed of 40 km/h and the other at 30 km/h, after how many hours will they meet?
(a)`2 (3)/(4)` hours
(b)`3 (1)/(2)` hours
(c)3 hours
(d)2 hours

Options

A. `2 (3)/(4)` hours
B. `3 (1)/(2)` hours
C. 3 hours
D. 2 hours

Answer

To solve the problem, we need to determine how long it will take for two cars traveling towards each other to meet. Here’s a step-by-step solution:

### Step 1: Understand the Problem
We have two cars starting from two different places, A and B, which are 245 km apart. One car travels at a speed of 40 km/h and the other at 30 km/h.

### Step 2: Calculate the Relative Speed
Since the cars are moving towards each other, we can add their speeds to find the relative speed:
- Speed of Car A = 40 km/h
- Speed of Car B = 30 km/h

**Relative Speed = Speed of Car A + Speed of Car B**
\[ \text{Relative Speed} = 40 \, \text{km/h} + 30 \, \text{km/h} = 70 \, \text{km/h} \]

### Step 3: Use the Formula for Time
To find the time taken for the two cars to meet, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

### Step 4: Substitute the Values
We know the distance between A and B is 245 km and the relative speed is 70 km/h:
\[ \text{Time} = \frac{245 \, \text{km}}{70 \, \text{km/h}} \]

### Step 5: Perform the Division
Now, we will perform the division:
\[ \text{Time} = \frac{245}{70} \]
To simplify:
- 245 divided by 70 can be calculated as follows:
\[ 245 \div 70 = 3.5 \, \text{hours} \]

### Step 6: Convert the Decimal to a Fraction
3.5 hours can be expressed as:
\[ 3.5 = 3 \frac{1}{2} \, \text{hours} \]

### Conclusion
The two cars will meet after **3 (1/2) hours**. Thus, the correct answer is option (b) 3 (1/2) hours.

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