A cyclist cycles non-stop from A to B, a distance of 14 km at a certain average speed If - Maths - Surface Areas and Volumes

Question

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 per he takes 1/3hr
more to cover the same distance find the original
speed

Ajanta Trivedi · Accepted Answer

let the original speed of the cyclist be x km/hr.

from A to B distance = 14 km.

time taken to travel from A to B = distance/speed = 14/x hr

if the speed reduces by 1km/hr the new speed = x-1 km/hr

$\frac{14}{x - 1} = \frac{14}{x} + \frac{1}{3} \frac{14}{x - 1} - \frac{14}{x} = \frac{1}{3} 14 [\frac{1}{x - 1} - \frac{1}{x}] = \frac{1}{3} 14 [\frac{x - (x - 1)}{x (x - 1)}] = \frac{1}{3} \frac{14}{x (x - 1)} = \frac{1}{3}$

$x (x - 1) = 42 x^{2} - x - 42 = 0 x^{2} - 7 x + 6 x - 42 = 0 (x - 7) (x + 6) = 0$

x= 7 or x=-6

since the speed can not be negative. the original speed of the cyclist is 7 km/hr.

hope this helps you.

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 per he takes 1/3hr more to cover the same distance. find the original speed