Thanks @ nov79,

Just now got a detailed explanation for this. This is in addition to the above explanation.

Let's say that P is traveling at a speed of 300 M/H and Q at a speed of 200 M/H, together the speed is 500 M/H.

The meetings:

1)When P meets Q for the first time, he would have travelled 3/5 (1000) = 600 m. --- First meeting.

2nd , 3rd and fourth meeting.

Between any two consecutive meetings, any two people separated by a certain distance initially, would be together covering twice the initial distance between them, if they start running simultaneously in opposite directions and move to and fro between their initial starting points.

Hence P and Q would have together cover 2000 m between the 2nd and 3rd as well as 3rd and 4th meeting. Therefore P takes 4 hrs to meet 2nd, 3rd and 4th meeting each. So distance travelled in each meeting = 300*4=1200m each.

Total distance P covers when he meets Q for the fourth time = 600+ 1200+1200+1200 = 4200 m

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