How to find the average speed? Very simple! It is necessary to divide the entire path by the time that the object of movement was on the way. In other words, you can define the average speed as the arithmetic average of all the speeds of the object. But there are some nuances in solving problems in this area.
For example, to calculate the average speed, this variant of the problem is given: the traveler first traveled at a speed of 4 km per hour for an hour. Then a passing car "picked up" him, and the rest of the way he drove in 15 minutes. Moreover, the car was traveling at a speed of 60 km per hour. How to determine the average travel speed of a traveler?
You should not just add 4 km and 60 and divide them in half, this will be the wrong decision! After all, the paths traveled on foot and by car are unknown to us. So, first you need to calculate the whole path.
The first part of the path is easy to find: 4 km per hour X 1 hour = 4 km
There are minor problems with the second part of the journey: speed is expressed in hours, and travel time in minutes. This nuance often makes it difficult to find the right answer when questions are asked how to find the average speed, path or time.
Express 15 minutes in hours. For this 15 min: 60 min = 0.25 hours. Now let’s calculate which traveler traveled along the way?
60 km / h X 0.25h = 15 km
Now finding the entire path traveled by a traveler is not difficult: 15 km + 4 km = 19 km.
Travel time is also quite easy to calculate. This is 1 hour + 0.25 hours = 1.25 hours.
And now it’s already clear how to find the average speed: you need to divide the entire path by the time that the traveler spent on overcoming it. That is, 19 km: 1.25 hours = 15.2 km / h.
There is such a joke in the subject. A man rushing to the railway station asks the owner of the field: “Can I go to the station through your station? I'm a little late and would like to shorten my path by going directly. Then I will definitely be in time for the train, which leaves at 16 hours and 45 minutes! ” “Of course you can shorten your path by going through my meadow!” And if my bull will notice you there, then you will even have time for that train, which leaves at 16 hours 15 minutes. ”
This comical situation, meanwhile, is most directly related to such a mathematical concept as the average speed of movement. After all, a potential passenger is trying to shorten his journey for the simple reason that he knows the average speed of his movement, for example, 5 km per hour. And the pedestrian, knowing that the detour along the asphalt road is 7.5 km, having made mentally simple calculations, understands that he will need one and a half hours (7.5 km: 5 km / h = 1.5 hours).
He, having left the house too late, is limited in time, and therefore decides to shorten his path.
And here we are faced with the first rule, which dictates to us how to find the average speed: taking into account the direct distance between the extreme points of the path or precisely calculating the trajectory of movement. From the foregoing, it is clear to everyone: a calculation should be made, taking into account precisely the trajectory of the path.
Having shortened the path, but without changing its average speed, the object in the person of a pedestrian receives a gain in time. The farmer, assuming the average speed of a sprinter running away from an angry bull, also makes simple calculations and gives his own result.
Motorists often use the second, important, rule for calculating the average speed, which refers to the time spent on the road. This concerns the question of how to find the average speed in case the object has a stop along the way.
In this option, usually, if there are no additional clarifications, the total time, including stops, is taken for the calculation. Therefore, a car driver can say that his average speed in the morning on a free road is much higher than the average speed during rush hour, although the speedometer shows the same figure in both versions.
Knowing these figures, an experienced driver will never be late, having previously guessed what his average speed of movement in the city at different times of the day will be.