Question

A plane took off $1$ hour late from Vadodara. To reach in time at a distance of $1200km$, its speed is increased by $100km/h$. Find its usual speed.

Answer 1

Given: Distance $=1200km$

Let initial speed be $s$ and time be $t$

$s=\frac{1200}{t}$ (1)

When $t=t-1$ and $s=s+100$

(1) is changed to $s+100=\frac{1200}{t-1}$ (2)

Substituting (2) in (1)

$\frac{1200}{t}+100=\frac{1200}{t-1}$

Solving for t

$\frac{12}{t}+1=\frac{12}{t-1}$

$1=\frac{12}{t-1}-\frac{12}{t}$

$1=12(\frac{1}{t-1}-\frac{1}{t})$

$1=\left(\frac{12}{t^2-t}\right)$

$t^2-t-12=0$

$t=\frac{+1\pm \sqrt{1+48}}{2}$

$t=4or-3$

t cannot be negative hence$t=4$

From (1) $s=300$

Hence the usual speed $=300km/hr$