A bus leaves city MM and travels to city NN at a constant speed, at the same time another bus leaves city NN and travels to city MM at the same constant speed. After driving for 2 hours they meet at point PP. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point PP, what is the distance between the two cities

Distance between cities MM and NN is 96 miles

Step-by-step explanation:

If a bus leaves city MM and travels at constant speed to city NN and a second bus at the same time leaves city NN and at the same constant speed, then they have to meet at PP (middle point of the distance between MM and NN)

If next day one the buses do the return trip but one is delayed 24 minutes and the other leaves 36 minutes earlier and again they will go at the same constant speed, that means a difference of 1 hour between departures time  of buses and at the same time that hour of difference means 24 miles of traveled distance.

As the speed is the same, we conclude buses traveled at 24 miles/h, the point PP (middle point between MM and NN is 48 miles apart from any of the cities and total distance between cities is 96 miles

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