Discussion
A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance?
Answer: B
Add the times for the two portions.
\[ t = \frac{d/4}{26} + \frac{3d/4}{24} = \frac{d}{104} + \frac{d}{32} \]
Over the common denominator 416:
\[ t = \frac{4d + 13d}{416} = \frac{17d}{416} \]
\[ \bar{v} = \frac{d}{17d/416} = \frac{416}{17} = 24\tfrac{8}{17} \text{ kmph} \]
The average must lie between 24 and 26, and nearer 24 since three quarters of the distance is covered at that speed - a check that rules out anything below 24.
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