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Question

(A) Let the distance between place $A$ and place $B$ be $x\, km.$
For the cyclist:
The speed is constant at $12\, km/hr.$ The total distance covered

Vedclass · Accepted Answer

cyclist

Vedclass · Answer

(A) Let the distance between place $A$ and place $B$ be $x\, km.$
For the cyclist:
The speed is constant at $12\, km/hr.$ The total distance covered is $2x\, km.$
Time taken by the cyclist $= \frac{	ext{Total Distance}}{	ext{Speed}} = \frac{2x}{12} = \frac{x}{6}\, hours.$
For the sailor:
The boat travels downstream from $A$ to $B$ and upstream from $B$ to $A.$
Speed downstream $= 10 + 4 = 14\, km/hr.$
Speed upstream $= 10 - 4 = 6\, km/hr.$
Time taken by the sailor $= \frac{x}{14} + \frac{x}{6} = \frac{3x + 7x}{42} = \frac{10x}{42} = \frac{5x}{21}\, hours.$
Comparing the times:
To compare $\frac{x}{6}$ and $\frac{5x}{21},$ we find a common denominator $(42)$:
$\frac{x}{6} = \frac{7x}{42}$
$\frac{5x}{21} = \frac{10x}{42}$
Since $\frac{7x}{42} < \frac{10x}{42},$ the cyclist takes less time.
Therefore,the cyclist will return to place $A$ first.

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