A starts from X at 9 : 00 a.m. and reaches Y at 1 : 00 p.m. on the same day, B also starts from Y at 9 : 00 a.m.. and reaches X at 3 p.m. on the same day. Following the same routes as A. At what time do the two meet?

Correct option is A

Solution:

Calculate the time taken by A and B to travel.

A starts at 9:00 a.m. and reaches Y at 1:00 p.m., so A takes 4 hours.

B starts at 9:00 a.m. and reaches X at 3:00 p.m., so B takes 6 hours.

Assume the total distance between X and Y is D.

The speeds of A and B can be calculated as follows:
Speed of A = $$\frac{D }{ 4}$$​​
Speed of B = $$\frac{D }{ 6}$$​​

Calculate the relative speed when they are traveling towards each other.

The relative speed is:
Relative Speed = $$\frac{D}{4} + \frac{D}{6 }= \frac{5D}{12}$$​​

the time taken for A and B to meet.

Both start at 9:00 a.m., and they meet when they cover the distance D together. Let the time taken to meet be t.

Using the formula: Distance = Speed × Time, we get:
Distance Covered Together = Relative Speed × t = D

Substitute the relative speed: $$(\frac{5D}{12}) × t = D.$$​​

Simplify for t: t = $$\frac{12 }{5}$$​ = 2.4 hours.

Determine the meeting time.

2.4 hours after 9:00 a.m. is 9:00 + 2.4 hours = 11:24 a.m.

A and B will meet at 11:24 a.m.