FINDING THE AVERAGE SPEED IN ROUND TRIP
What is round trip?
Travelling in one direction at a certain rate of speed, and then returning along the same route at a different rate of speed is known as round trip.
Finding Average Speed
If a person travels from A to B at some speed, say x miles per hour. He comes back from B to A at different speed, say y miles per hour. Both the ways, he covers the same distance, but at different speeds.
Then, the formula is to find the average speed for the whole journey is given below.
= 2xy/(x + y)
The purpose of finding the average speed :
For example, a car traveling from one city to another will rarely move at a constant speed. It is more likely that the car's speed will fluctuate during the trip.
The car might travel at 50 mph for some time and then slow down to 20 mph. It's possible that at certain times, the car is even at full stop (such as, at a red light). To calculate the car's average speed, we don't really care about the fluctuations in its speed.
We only care about the total distance traveled by the car and the elapsed time to cover that distance.
Example 1 :
Mr. Brown drove at a speed of 96 km/hr to his office every morning. He returned from work at the speed of 72 km/hr. What was his average speed for the round trip?
Solution :
In both the ways, Mr. Brown covers the same distance.
Formula to find the average speed :
= 2xy/(x + y)
Substitute x = 96 and y = 72.
Average speed = (2 ⋅ 96 ⋅ 72)/(96 + 72)
= (2 ⋅ 96 ⋅ 72)/168
= (96 ⋅ 72)/84
= (8 ⋅ 72)/7
= 576/7
= 82.3 km/hr
Example 2 :
Mr. John drives at a constant speed of 108 km/h to his office every morning. He drives at a constant speed of 72 km/hr. for his return trip. What is his average speed for the round trip?
Solution :
In both the ways, Mr. John covers the same distance.
Average speed = 2xy/(x + y)
Substitute x = 108 and y = 72.
= (2 ⋅ 108 ⋅ 72)/(108 + 72)
= (2 ⋅ 108 ⋅ 72)/180
= (108 ⋅ 72)/90
= (6 ⋅ 72)/5
= 432/5
= 86.4 km/hr
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