Two friends, Farhan and Zoya, started from point F towards point Q at 10:00 am. Each of them, after reaching Q, immediately returned back to point P.

If Farhan took 6 hours and Zoya took 12 hours for the journey, then at what time did they cross each other?

Farhan and Zoya crossed each other at 2:00 pm. Farhan takes 6 hours to reach point Q, while Zoya takes 12 hours. Using their speeds and the distance, we calculated the time they would cross each other during their respective journeys.
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Answered by Anonymous | 2025-07-04

To solve the problem of when Farhan and Zoya crossed each other, we need to understand their movement along the path from point F to point Q and back.
Let's break down the information provided:

Farhan's Journey:

Farhan completes his journey from point F to point Q and back to point F in a total of 6 hours.
Therefore, the time taken for a one-way journey for Farhan is 2 6 ​ = 3 hours.


Zoya's Journey:

Zoya completes her journey from point F to point Q and back to point F in a total of 12 hours.
Therefore, the time taken for a one-way journey for Zoya is 2 12 ​ = 6 hours.


Relative Speed:

Let's denote the distance between point F and point Q as d .
Farhan's speed v F ​ = 3 d ​ since he takes 3 hours one-way.
Zoya's speed v Z ​ = 6 d ​ since she takes 6 hours one-way.


Time of Intersection:

Both started their journey at 10:00 am.
To find when they cross each other, we can set up the equation based on their relative speed:

v F ​ × t = ( d − v Z ​ × t )
Where t is the time in hours from 10:00 am.
Substituting the speeds:
3 d ​ × t = d − 6 d ​ × t
Solving for t :
3 d ​ × t + 6 d ​ × t = d
( 6 2 ​ + 6 1 ​ ) d × t = d
6 3 ​ d t = d
2 1 ​ d t = d
t = 2
Therefore, Farhan and Zoya cross each other 2 hours after 10:00 am.


Therefore, they cross each other at 12:00 pm.

Answered by danjohnbrain | 2025-07-06