Rahul starts on his journey at 5 pm at a constant speed so that he reaches his destination at 11 pm the same day. However, on his way, he stops for 20 minutes, and after that, increases his speed by 3 km per hour to reach on time. If he had stopped for 10 minutes more, he would have had to increase his speed by 5 km per hour to reach on time. His initial speed, in km per hour, was

Let the initial speed be v and the total distance be D, so the total travel time is D/v = 6 hours. After a 20 minute delay, the time left is (6 - v/3 - 1/3) hours, and increasing the speed by 3 km per hour gives the equation v * (6 - v/3 - 1/3) = D = 6v. Solving this system of equations derived from both scenarios yields an initial speed of 15 km per hour.

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