Over the weekend, a get-together has been scheduled at Gurmeet's

Gurmeet, Anuradha, Arunoday, Shrawan, Kartik, Priyanshu and Arvind are seven friends living along a straight road in the same manner as given starting with Gurmeet.

Shrawan lives 150 km away from Gurmeet and takes (p x p) min to reach Priyanshu. It takes Gurmeet 5 hours to reach Priyanshu who lives 250 km away from him. When Arunoday and Arvind move toward each other at (p x 4th smallest prime number) km/hr and (p x 3rd smallest prime number) km/hr respectively, they meet after 1 hr 35 min. Arunoday takes only 34 2/7 min to reach Shrawan. Anuradha who is 240 km away from Arvind crosses Kartik after 5 hr 40 min and meets Arvind after 8 hours from start. Kartik and Priyanshu meet after 24 minutes, if they start moving simultaneously towards each other with speed in ratio 3: 2 respectively.

Where p is positive root of p² - 7p - 30 = 0
Note: Speed of all remains constant.

Over the weekend, a get-together has been scheduled at Gurmeet's house, precisely at 9:00 pm. To calculate Kartik's departure time from his home, consider the time he will need to pause for 10 minutes at Anuradha's house, waiting for her. When should Kartik set out to reach Gurmeet's home on time?

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