Four vehicles travelled on a road with constant velocities. The car overtook the scooter at 12 o'clock, then met the bike at 14.00 and the motorcycle at 16.00. The motorcycle met the scooter at 17.00 then it overtook the bike at 18.00. At what time did the bike and the scooter meet?
Brian swims at twice the speed that a river is flowing, downstream from one moored boat to another and back again, taking 12 minutes altogether. How long would it have taken him in still water?
At Holborn underground station there is a very long escalator. Two people are in a hurry and so climb the escalator as it is moving upwards, thus adding their speed to that of the moving steps. ... How many steps are there on the escalator?
The reason the average of the average speeds isn't the overall average speed is because the journey time isn't the same there and back . . . . but the distance is, and that's useful if instead I use the reciprocal of the rate.
Speed is a rate (the rate at which distance changes as time passes) and any rate can be considered in it's reciprocal form (the rate at which time passes per unit distance)
The distance is the same so adding the reciprocal of the speeds and then dividing by two does give me the reciprocal of the overall average speed.
and this gives the answer 75 mph too.