Question

Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q at 8 a.m. at the speed of 25 km/hr. Another rider starts from Q towards P at 9 a.m. at the speed of 20 km/hr. Find at what time they will cross each other.

• A. 2:45 p.m.
• B. 2:30 p.m.
• C. 1:35 p.m.
• D. 1:15 p.m.

Hint:

In problems involving two objects moving towards each other, use the formula for relative speed to find the time they meet.

Answer 1

The Correct Option is D

Step 1: The total distance between the two towns is 275 km. 
Step 2: The two riders are moving towards each other, so we can calculate the relative speed: \[ \text{Relative speed} = 25 + 20 = 45 \, \text{km/hr} \] Step 3: The time taken to meet each other is: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{275}{45} = 6.11 \, \text{hours} \] 
Step 4: Since the first rider starts at 8 a.m., the time of meeting will be: \[ 8:00 + 6.11 \, \text{hours} = 1:15 \, \text{p.m.} \] Thus, they will cross each other at 1:15 p.m.