If A starts from P with, speed 60 km/hr at 8:00 am and B starts with speed 70 km/hr at 8 : 30 am from Q and the total distance between P and Q is 680 km, find at what time they will cross each other.

Options

A. 1:00 pm
B. 1:30pm
C. 12:30pm
D. 3:00pm

Answer

To solve the problem step by step, we need to determine when A and B will meet as they travel towards each other from points P and Q, respectively.

### Step 1: Determine the time A travels before B starts
A starts at 8:00 AM and B starts at 8:30 AM. Therefore, A travels for 30 minutes (or 0.5 hours) before B starts.

### Step 2: Calculate the distance A covers in 30 minutes
A's speed is 60 km/hr. The distance covered by A in 0.5 hours is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/hr} \times 0.5 \, \text{hr} = 30 \, \text{km} \]

### Step 3: Determine the remaining distance between A and B when B starts
The total distance between P and Q is 680 km. After A has traveled 30 km, the remaining distance between A and B when B starts is:
\[ \text{Remaining Distance} = 680 \, \text{km} - 30 \, \text{km} = 650 \, \text{km} \]

### Step 4: Calculate the relative speed of A and B
A travels at 60 km/hr and B travels at 70 km/hr. Since they are moving towards each other, their relative speed is:
\[ \text{Relative Speed} = \text{Speed of A} + \text{Speed of B} = 60 \, \text{km/hr} + 70 \, \text{km/hr} = 130 \, \text{km/hr} \]

### Step 5: Calculate the time taken to meet after B starts
Now, we can find the time it takes for A and B to meet after B starts. The time taken to cover the remaining distance of 650 km at a relative speed of 130 km/hr is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{650 \, \text{km}}{130 \, \text{km/hr}} = 5 \, \text{hours} \]

### Step 6: Determine the time they meet
B starts at 8:30 AM, and they take 5 hours to meet. Therefore, they will meet at:
\[ 8:30 \, \text{AM} + 5 \, \text{hours} = 1:30 \, \text{PM} \]

### Final Answer:
A and B will cross each other at **1:30 PM**.

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