A car left Lahore for Kabul at 5 pm. Traveling a speed of 60 km/h. Another car left Kabul for Lahore at 7 pm, traveling a speed of 70 km/h. If the distance between Kabul and Lahore is 380 km, at what time will the cars cross each other ?

Options

A. 9:00 pm
B. 9:32pm
C. 9:43 pm
D. 9:35 pm

Answer

To solve the problem, we will break it down step by step.

### Step 1: Determine the time difference between the two cars leaving.
The first car leaves Lahore for Kabul at 5 PM, and the second car leaves Kabul for Lahore at 7 PM. This means the first car has a 2-hour head start.

**Hint:** Always note the time difference when two objects start moving at different times.

### Step 2: Calculate the distance traveled by the first car before the second car starts.
The first car travels at a speed of 60 km/h. In the 2 hours before the second car starts, it travels:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/h} \times 2 \, \text{h} = 120 \, \text{km} \]

**Hint:** Use the formula for distance to calculate how far an object travels in a given time.

### Step 3: Determine the remaining distance between the two cars when the second car starts.
The total distance between Lahore and Kabul is 380 km. After the first car has traveled 120 km, the remaining distance is:
\[ \text{Remaining Distance} = 380 \, \text{km} - 120 \, \text{km} = 260 \, \text{km} \]

**Hint:** Subtract the distance traveled from the total distance to find the remaining distance.

### Step 4: Calculate the relative speed of the two cars.
The first car is traveling towards Kabul at 60 km/h, and the second car is traveling towards Lahore at 70 km/h. Therefore, their relative speed is:
\[ \text{Relative Speed} = 60 \, \text{km/h} + 70 \, \text{km/h} = 130 \, \text{km/h} \]

**Hint:** When two objects move towards each other, their speeds add up.

### Step 5: Calculate the time taken for the two cars to meet.
Using the formula for time, where time is equal to distance divided by speed:
\[ \text{Time} = \frac{\text{Remaining Distance}}{\text{Relative Speed}} = \frac{260 \, \text{km}}{130 \, \text{km/h}} = 2 \, \text{h} \]

**Hint:** Remember that time can be calculated using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).

### Step 6: Determine the time at which the cars will cross each other.
The second car starts at 7 PM and takes 2 hours to meet the first car. Therefore, they will cross each other at:
\[ 7 \, \text{PM} + 2 \, \text{h} = 9 \, \text{PM} \]

**Hint:** Add the time taken to the start time of the second car to find the meeting time.

### Final Answer:
The cars will cross each other at **9 PM**.