Calculating Average Speeds:
There are 2 ways to calculate average speeds,
1. Typical Distance-Time formula: (Traditional way - RECOMMENDED)
Assume S1 and S2 are the speeds of 2 trips. Distance d is the same for both the trips.
Assume T as the total time taken for both the trips.
Time taken = Distance / Speed.
For this scenario,
Total Time Taken = (Distance of Trip 1/Speed of Trip 1) + (Distance of Trip 2/Speed of Trip 2)
T = d/S1 + d/S2
T = (d*S1 + d*S2) / (S1*S2)
T = d*(S1+S2) / (S1*S2)
Now calculate Average speed using Total Distance and Total Speed,
Avg Speed = Total Distance / Total Time Taken
Avg Speed = 2d / T .......... [2d is the distance of Trip 1 and 2]
Sub. T = d*(S1+S2) / (S1*S2) in the equation,
Avg Speed = 2d*(S1*S2) / d*(S1+S2)
Avg Speed for the entire trip = 2*(S1*S2) / (S1+S2) .... [Cancelling out d]
NOTE: You don't need to solve this to get average speed. You can apply this formula straight away. Just wanted to show you how the formula is arrived.
2. A cool shortcut: (UNORTHODOX Approach)
Assuming Distance is the same for both the trips. S1 and S2 are the speeds of Trips 1 and 2.
Step i:
Form S1:S2 and reduce the ratio as much as possible to S3:S4.
Then, add the parts of ratio -- S3+S4
Step ii:
|S1-S2| / (S3+S4) = N
Step iii:
S1 + (S3*N) = Avg Speed for the entire trip.
Example:
Calculate Avg Speed of 20 mph and 200 mph
Step i:
20:200 = 1:10 = 1+10 = 11 parts.
Step ii:
|20-200| / 11 = 16.36
Step iii:
20 + (1*16.36) = 36.36 mph -- [Average Speed for the entire trip].
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