A car leaves station `X` for station `Y` every 10 min. The distance between `X` and `Y` is `60km`. The car travels at speed `60km//h`. A man drives a car from `Y` towards `X` at speed `60km//h`. If he starts at the moment when first car leaves station `X`, how many cars would he meet om route?

Options

A. 20
B. 7
C. 10
D. 5

Answer

To solve the problem, we need to determine how many cars the man will meet while driving from station Y to station X. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the scenario
- A car leaves station X for station Y every 10 minutes.
- The distance between X and Y is 60 km.
- The speed of the cars (both the one leaving X and the one driven by the man from Y) is 60 km/h.

### Step 2: Calculate the time taken by the car to travel from X to Y
- The time taken by a car to travel the distance of 60 km at a speed of 60 km/h can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{60 \text{ km}}{60 \text{ km/h}} = 1 \text{ hour} \]

### Step 3: Determine the frequency of car departures
- A car leaves every 10 minutes. In terms of hours, this is:
\[ 10 \text{ minutes} = \frac{10}{60} \text{ hours} = \frac{1}{6} \text{ hours} \]

### Step 4: Calculate the distance covered by the departing cars in 10 minutes
- The distance covered by a car in 10 minutes (or \(\frac{1}{6}\) hours) at a speed of 60 km/h is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 60 \text{ km/h} \times \frac{1}{6} \text{ hours} = 10 \text{ km} \]
- This means that every 10 minutes, a new car leaves station X, and each car is 10 km apart from the previous one.

### Step 5: Calculate how many cars the man will meet
- The man starts driving from station Y towards station X at the same speed of 60 km/h.
- Since the total distance between X and Y is 60 km, we can divide this distance into segments of 10 km (the distance between the cars).
- The number of segments (or cars) he will meet on his way is:
\[ \text{Number of segments} = \frac{60 \text{ km}}{10 \text{ km}} = 6 \]
- Additionally, he will also meet the first car that has just left station X.

### Step 6: Total number of cars met
- Therefore, the total number of cars the man will meet is:
\[ 6 \text{ (cars)} + 1 \text{ (the first car)} = 7 \]

### Final Answer
The man will meet **7 cars** on his route from Y to X.

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