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Question
Q:- A car travels with the following speeds with the following durations:
[1] with 8 kilometers/hour for 2 hours
[2] with 13 kilometers/hour for 2 hours
[3] with 20 kilometers/hour for 2 hours
[4] with 16 kilometers/hour for 2 hours
[5] with 9 kilometers/hour for 2 hours
[6] with 15 kilometers/hour for 2 hours
[7] with 17 kilometers/hour for 2 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 = 8 x 2 + 13 x 2 + 20 x 2 + 16 x 2 + 9 x 2 + 15 x 2 + 17 x 2 kilometers
= (8 + 13 + 20 + 16 + 9 + 15 + 17) x 2 kilometers
= 98 x 2 kilometers = 196 kilometers
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Step : 2
Total time travelled = 2 + 2 + 2 + 2 + 2 + 2 + 2 hours
= 2 x 7 hours = 14 hours
=>mean speed = total distance / total time
=>mean speed = (8 + 13 + 20 + 16 + 9 + 15 + 17) x 2 kilometers / 2 x 7 hours
=>mean speed = (8 + 13 + 20 + 16 + 9 + 15 + 17) / 7 kilometers/hour
=> mean speed = 98 / 7 = 14 kilometers/hour
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Step : 3
In (8 + 13 + 20 + 16 + 9 + 15 + 17)/7
(8 + 13 + 20 + 16 + 9 + 15 + 17) is the sum of all the speeds and 7 is the count of all the speeds
So, (8 + 13 + 20 + 16 + 9 + 15 + 17) divided by 7 is also the mathematical average of the speeds
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