Average Speed = Total Distance/Total Time
No matter which formula you choose to use, it will always boil down to this one. Keeping this in mind, let's discuss the various formulas we come across:
1. Average Speed = (a + b)/2
Applicable when one travels at speed a for half the time and speed b for other half of the time. In this case, average speed is the arithmetic mean of the two speeds.
2. Average Speed = 2ab/(a + b)
Applicable when one travels at speed a for half the distance and speed b for other half of the distance. In this case, average speed is the harmonic mean of the two speeds. On similar lines, you can modigy this formula for one-third distance.
3. Average Speed = 3abc/(ab + bc + ca)
Applicable when one travels at speed a for one-third of the distance, at speed b for another one-third of the distance and speed c for rest of the one-third of the distance.
Note that the generic Harmonic mean formula for n numbers is
Harmonic Mean = n/(1/a + 1/b + 1/c +.....)
4. You can also use weighted averages. Note that in case of average speed, the weight is always 'time'. So in case you are given the average speed, you can find the ratio of time as
t1/t2 = (a - Avg)/(Avg - b)
As you already know, this is just our weighted average formula.
Now, let's look at some simple questions where you can use these formulas
No matter which formula you choose to use, it will always boil down to this one. Keeping this in mind, let's discuss the various formulas we come across:
1. Average Speed = (a + b)/2
Applicable when one travels at speed a for half the time and speed b for other half of the time. In this case, average speed is the arithmetic mean of the two speeds.
2. Average Speed = 2ab/(a + b)
Applicable when one travels at speed a for half the distance and speed b for other half of the distance. In this case, average speed is the harmonic mean of the two speeds. On similar lines, you can modigy this formula for one-third distance.
3. Average Speed = 3abc/(ab + bc + ca)
Applicable when one travels at speed a for one-third of the distance, at speed b for another one-third of the distance and speed c for rest of the one-third of the distance.
Note that the generic Harmonic mean formula for n numbers is
Harmonic Mean = n/(1/a + 1/b + 1/c +.....)
4. You can also use weighted averages. Note that in case of average speed, the weight is always 'time'. So in case you are given the average speed, you can find the ratio of time as
t1/t2 = (a - Avg)/(Avg - b)
As you already know, this is just our weighted average formula.
Now, let's look at some simple questions where you can use these formulas
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