Is my solution of this time and distance problem correct or wrong?

Question

P and Q start running in opposite directions (towards each other) on a circular track starting at diametrically opposite points. They first meet after P has run for 75m and then they next meet after Q has run 100 m after their first meeting. Assume that both of them are running a constant speed. The length of the track (in metre) is:

a)70 b)175 3)250 4)350

my solution

let p and q be speed of P and Q respectively and 2d be circumference since both start at diametrically opposite points so they meet at same time that is

75/p = (d-75)/q .....1

and Q has run 100m after first meeting so P will run 2d - 100 for next meeting

hence 100/q = (2d-100)/p ......2

solving 1 and 2 d is 125m , so 2d = 250m

is my solution correct or wrong ? while answer is 350 here is the link http://www.lofoya.com/Aptitude-Questions-And-Answers/Time-Speed-and-Distance/l1p6.htm check question 27 with solution

Answer 1

Dividing these into two separate runs on a straight track: When the distance between them is $d$, then $P$ has to run $75$ meters before they meet.

When the distance between them is $2d$ then naturally, $P$ has to run twice as far before they meet, so he runs $150$ meters. $Q$ runs $100$ meters, and their sum is the total circumference $250$.

The solution in the link is for some reason assuming that the two are running at the same speed, rather than separate, constant speeds, but I still don't quite follow the argument they make.

Answer 2

Your solution is correct, but the answer in the link you have provided is wrong, and here's why. If runners $P$ and $Q$ both ran for the same amount of time at the same speed, then $P$ and $Q$ would've traveled each 75 meters upon their first meeting, and because totally they traveled half the tracks distance, the total distance of the circular track is 300 meters.

The link's solution is also inconsistent with the second statement: $P$ and $Q$ meet again after $Q$ has traveled 100 meters from their first meeting. Assuming that $P$ and $Q$ both have traveled 75 meters during their first encounter, they will both run in opposite directions at the same speed for the same amount of time, so both runners actually run half the track's distance when they meet for the second time, which is 150 meters, so the second statement should say after $Q$ ran 150 meters, not 100.