Question

Yashvi rides a bicycle at a uniforn speed. If the speed had been 4KM/HR more, it would have taken 1hour less to travel 48km distance. Determine her speed

Answer 1

$\huge\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\blue{W}\green{E}\pink{R}}}}</p><p></p><p>$

$\large\bold\red{case \: 1}$

$Let \: the \: uniform \: speed \: of \: bicycle \: be \: x \: km/hr. \\ </p><p>Distance \: covered = 48 \: km. \\ </p><p>So, time \: taken, t_1 = \dfrac{48}{x}$

$\large\bold\red{case \: 2}$

$Now, \: Speed \: is \: 4 \: km/hr \: more. \\ </p><p>So, \: now \: speed = (x + 4) km/hr\\ </p><p>Distance \: covered \: = 48 \: km \\ </p><p>Time \: taken, \: t_2 = \dfrac{48}{x + 4} </p><p>$

$\large\bold\red{According \: to \: statement }$

$\large\bold \blue{t_1 - t_2 = 1}$

$= > \frac{48}{x} - \frac{48}{x + 4} = 1 \\ = > \: \frac{48(x +4 ) - 48}{x(x + 4)} = 1\\ = > \frac{48x + 192 - 48x}{ {x}^{2} + 4x} = 1 \\ = > \: 192 = {x}^{2} + 4x \\ \\ = > \: {x}^{2} + 4x - 192 = 0 \\ = > \: {x}^{2} + 16x - 12x - 192 = 0 \\ = > x(x + 16) - 12(x + 16) = 0 \\ = > \: (x + 16)(x - 12) = 0 \\ = > x = 12 \: or \: x = - 16 \\ so \: it \: means \: x = 12$

$\boxed{ \large{ \mathfrak{So, \: the \: speed \: of \: bicycle \: is \: 12 \: km/hr}}}$