Ali,while driving to school,computes the aver | vedclass

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Question

(A) Let the distance between Ali's home and school be $x$.During the trip to school:Distance $= x$,Speed $= 20 \, km \, h^{-1}$.Time taken $t_1 = \fra

Vedclass · Accepted Answer

$24 \, km \, h^{-1}$

Vedclass · Answer

(A) Let the distance between Ali's home and school be $x$.During the trip to school:Distance $= x$,Speed $= 20 \, km \, h^{-1}$.Time taken $t_1 = \frac{x}{20} \, h$.During the return trip:Distance $= x$,Speed $= 30 \, km \, h^{-1}$.Time taken $t_2 = \frac{x}{30} \, h$.Average speed is defined as the total distance divided by the total time taken:Average Speed $= \frac{	ext{Total Distance}}{	ext{Total Time}} = \frac{x + x}{t_1 + t_2} = \frac{2x}{\frac{x}{20} + \frac{x}{30}}$.Calculating the denominator:$\frac{x}{20} + \frac{x}{30} = \frac{3x + 2x}{60} = \frac{5x}{60} = \frac{x}{12}$.Therefore,Average Speed $= \frac{2x}{x/12} = 2x 	imes \frac{12}{x} = 24 \, km \, h^{-1}$.

Ali,while driving to school,computes the average speed for his trip to be $20 \, km \, h^{-1}$. On his return trip along the same route,there is less traffic and the average speed is $30 \, km \, h^{-1}$. What is the average speed for Ali's entire trip?

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