1.

A cyclist cycles non-stop from A to B, a distance of 14 km at a certain average speed. If his average speed reduces by 1 km / hr, then he takes \(\frac13\)hour more to cover the same distance. What was the original average speed of the cyclist?

Answer»

Let the original average speed of the cyclist be x km/hr.

Then, \(\frac{14}{(x-1)}-\frac{14}{x}=\frac13\) ⇒ \(\frac{14x-14(x-1)}{x(x-1)}\) = \(\frac13\)

⇒ \(\frac{14}{x^2-x}=\frac13\) ⇒ x2 – x – 42 = 0 ⇒ x2 – 7x + 6x – 42 = 0 

⇒ x(x – 7) + 6(x – 7) = 0 ⇒ (x – 7) (x + 6) = 0 ⇒ x = 7 or –6 

Since speed cannot be negative, x = 7 km/hr


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