Average Speed is important to understand the rate at which a journey takes place. Throughout a journey, the speed may vary from time to time. In that case, finding the average speed becomes important to have an estimate of the rate at which the journey is completed. Here we will see some special cases and shortcuts that we can use to find the average speed in less than a minute. Let us begin by calculating the formula for the average speed and then solve some examples with the help of this formula.
The speed of an object is found out by dividing the distance that the object covers by the time in which the object takes to cover this distance. If ‘D’ is the distance traveled in some time ‘T’ then the speed of the object for this journey or ‘s’ is equal to s = D/T.
This is the simplest case. But what if there is an object that covers part of its journey with one speed and the other part with another speed? Let us say a train goes from station A to B in 2 minutes and from B to C in 3 minutes. If the distance between any two stations is 6km, what is the speed of the train?
Answer: Here you can’t use the formula directly because as you may have observed the train has a different speed from A to B than from B to C. In this case when a body has different speed during different parts of the journey, we define the average speed as:
Average Speed = (Total distance covered throughout the journey)/(Total time taken for the journey)
Let the body cover a distance ‘a’ in time t1, then a distance b in time t2, c in time t3 and so on, then the average speed of the body is found out by the following ratio:
Average speed = (a + b + c + …)/ (t1 + t2 + t3 + …). Let us see some examples now.
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Some Solved Examples
Example 1: A truck goes from Haryana to Bangalore with an average speed of 60 km/hr. The journey takes 30 hours. It returns from Bangalore to Haryana on the same road with an average speed of 40 km/hr. What was the average speed of the truck during the roundtrip?
A) 50 km/hr B) 55 km/hr C) 48 km/hr D) 52 km/hr
Answer: You may be tempted to find the average speed by summing up the speed and dividing by 2. That is wrong because the average speed is the total distance divided by the total time. Let us find the distance first from Haryana to Bangalore. This can be done as follows:
Distance = (Speed)×(Time). Thus we can say that Distance = 60×30 = 1800 kilometers. Now we have to find the time taken to travel from Bangalore to Haryana. We can write:
Time = Distance / speed = 1800/40 = 45 hours. Thus we can find the average speed as:
Average Speed = (Total distance)/(Total Time) = (1800 + 1800)/(30 + 45) = 3600/75 = 48 km/hr. Hence the correct option here is C) 48 km/hr.
So to find the average speed never use the formula of the averages but try to find the total distance covered and the total time taken. Let us see a few more examples where the journey is completed in three stages.
Practice Average Practice Questions here
Three Stage Journey
Example 2: A person travels from Mumbai to Goa in exactly 8 hours with a speed of 120 km/hr. From Goa, the person travels to Delhi in 34 hours. If the distance from Goa to Delhi was 2000 km, how long will it take to get from Delhi to Bombay if the person maintains the speed equal to the average speed? The distance from Delhi to Bombay is 1400 km.
Answer: This is a three-stage journey. We will form a distance-speed-time table for every stage of the journey. It should make it easier for us.
|Distance||?||2000 km||1400 km|
|Time||8 hours||34 hours||?|
We don’t have to find the individual speeds for the two stages of the journey. We just want the average speed. To find that we have to find the total distance and the total time. We do have the distance and the time for the second stage so let us get it for the first stage too.
For the first stage, the time can be found by Distance = Speed × Time = 120×8 = 960 km. So the total distance is = (960 + 2000) = 2960 km.
Now the total time taken for the journey = 8 + 34 hours = 42 hours. Always make sure that you check the units. The units throughout the question should be uniform.
Thus the average speed = 2960/42 = 70.48 km/hr. Thus this is the speed that the person has to maintain from Delhi to Bombay. The time taken for this journey is = Distance / Speed. In other words, we can write:
Time taken = 2960/70.48 = 41.99 hours ≈ 42 hours.
Q 1: A speeding car traveling at 40 km/hr decides to slow down to 30 km/hr after covering half the distance. What is the average speed?
A) 34.29 km/h B) 35.36 km/hr C) 36.32 km/hr D) 33.21 km/hr
Ans: A) 34.29 km/h
Q 2: A car travels with the following speed and distance:
|100 km/hr||110 km/hr||120 km/hr||130 km/hr|
|120 km||130 km||140 km||150 km|
A) 115 km/hr B) 112 km/hr C) 1.17 km/hr D) 2.71 km/hr
Ans: C) 1.17 km/hr