Question

A car when starting from rest, travels the first twentieth of a km at 9 La-km per hour and the next three twentieth of at respectively 12, 18 and 36 km per hour. Two students found its average speed over the first fifty of a km. 24 respectively at 18.75 and 14.4 km per hour. Which do you think is the correct answer and why?
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Answer 1

Answer:-

Time taken in first twentieth of a km = $\frac{1/20}{9}$ = $\frac{1}{180}$hrs.

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Time taken in second twentieth of a km = $\frac{1/20}{12}$ = $\frac{1}{240}$hrs.

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Time taken in third twentieth of a km =$\frac{1/20}{18}$ = $\frac{1}{360}$hrs.

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Time taken in fourth twentieth of a km = $\frac{1/20}{36}$ = $\frac{1}{720}$hrs.

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Therefore, Total time taken in traveling $\frac{1}{5}$ of a km = $\frac{1}{180}+\frac{1}{240}+\frac{1}{360}+\frac{1}{720}$ = $\frac{1}{72}$hrs

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$\therefore$Average Speed over the first fifth of a km = $\frac{1/5}{1/72}$=$\frac{72}{5}$=14.4 km/h.

So,the Second Student is correct. Ans.

Answer 2

Answer:-

Time taken in first twentieth of a km

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Time taken in second twentieth of a km = $\frac{1/20}{12}$ = $\frac{1}{240}$hrs.

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Time taken in fourth twentieth of a km = $\frac{1/20}{36}$ = $\frac{1}{720}$hrs.

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Therefore, Total time taken in traveling $\frac{1}{5}$ of a km = $\frac{1}{180}+{1}{240}+{1}{360}+{1}{720}$ = $\frac{1}{72}$hrs

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