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Question
Q:- A car travels with the following speeds with the following durations:
[1] with 20 kilometers/hour for 8 hours
[2] with 17 kilometers/hour for 8 hours
[3] with 8 kilometers/hour for 8 hours
[4] with 4 kilometers/hour for 8 hours
[5] with 14 kilometers/hour for 8 hours
[6] with 7 kilometers/hour for 8 hours
[7] with 14 kilometers/hour for 8 hours
[8] with 9 kilometers/hour for 8 hours
[9] with 16 kilometers/hour for 8 hours
Find [1] average speed , and [2] observe that average speed is average of the speeds when time durations are the same.
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Step : 1
Total distance travelled = 20 x 8 + 17 x 8 + 8 x 8 + 4 x 8 + 14 x 8 + 7 x 8 + 14 x 8 + 9 x 8 + 16 x 8 kilometers
= (20 + 17 + 8 + 4 + 14 + 7 + 14 + 9 + 16) x 8 kilometers
= 109 x 8 kilometers = 872 kilometers
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Step : 2
Total time travelled = 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 hours
= 8 x 9 hours = 72 hours
=>mean speed = total distance / total time
=>mean speed = (20 + 17 + 8 + 4 + 14 + 7 + 14 + 9 + 16) x 8 kilometers / 8 x 9 hours
=>mean speed = (20 + 17 + 8 + 4 + 14 + 7 + 14 + 9 + 16) / 9 kilometers/hour
=> mean speed = 109 / 9 = 12.111111111111 kilometers/hour
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Step : 3
In (20 + 17 + 8 + 4 + 14 + 7 + 14 + 9 + 16)/9
(20 + 17 + 8 + 4 + 14 + 7 + 14 + 9 + 16) is the sum of all the speeds and 9 is the count of all the speeds
So, (20 + 17 + 8 + 4 + 14 + 7 + 14 + 9 + 16) divided by 9 is also the mathematical average of the speeds
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