Distance between two points A and B is 110 km. A motor-cycle rider starts from A towards B at 7 am at a speed of 20 km/hr. Another motor-cycle rider starts from B towards A at 8 am at a speed of 25 km/hr. Find when will they cross each other.

Options

A. `11` am
B. `9:30` am
C. `8:30` am
D. `10` am

Answer

To solve the problem step by step, we will break down the information given and calculate when the two motorcycle riders will meet.

### Step 1: Understand the problem
- Distance between points A and B = 110 km
- Rider from A starts at 7 AM with a speed of 20 km/hr.
- Rider from B starts at 8 AM with a speed of 25 km/hr.

### Step 2: Calculate the distance covered by the first rider before the second rider starts
The first rider starts at 7 AM and the second rider starts at 8 AM. Therefore, the first rider travels for 1 hour before the second rider starts.

Distance covered by the first rider in 1 hour:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 20 \text{ km/hr} \times 1 \text{ hr} = 20 \text{ km} \]

### Step 3: Calculate the remaining distance between the two riders when the second rider starts
Initially, the distance between A and B is 110 km. After the first rider has traveled 20 km, the remaining distance is:
\[ \text{Remaining Distance} = 110 \text{ km} - 20 \text{ km} = 90 \text{ km} \]

### Step 4: Calculate the relative speed of the two riders
The first rider is traveling towards B at 20 km/hr, and the second rider is traveling towards A at 25 km/hr. Therefore, the combined speed (relative speed) of both riders is:
\[ \text{Relative Speed} = 20 \text{ km/hr} + 25 \text{ km/hr} = 45 \text{ km/hr} \]

### Step 5: Calculate the time taken to meet after the second rider starts
To find the time taken for the two riders to meet after the second rider starts, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
Substituting the values:
\[ \text{Time} = \frac{90 \text{ km}}{45 \text{ km/hr}} = 2 \text{ hours} \]

### Step 6: Calculate the total time from the start of the first rider
The first rider started at 7 AM and traveled for 1 hour before the second rider started. After that, they took 2 more hours to meet. Therefore, the total time from 7 AM is:
\[ \text{Total Time} = 1 \text{ hour} + 2 \text{ hours} = 3 \text{ hours} \]

### Step 7: Determine the time they meet
Adding the total time to the starting time of the first rider:
\[ \text{Meeting Time} = 7 \text{ AM} + 3 \text{ hours} = 10 \text{ AM} \]

### Final Answer
The two motorcycle riders will cross each other at **10 AM**.

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