Question

If the speed of a car is decreased by 8$km/h$ , it takes 1 hour more toover a distance of 240$km.$ Find the original speed of the car.

Answer 1

Let the speed of car be $x\text{kmph}$

Let it takes Time $t$ hrs to cover the distance of $240km$

$⟹xt=240\cdots \left(1\right)$

speed is decreased by $8⟹x-8$

Time is increased by $1⟹t+1$

it covers the same distance so $(x-8)(t+1)=240xt+x-8t-8=240$

From $\left(1\right)⟹x-8t-8=0x=8t+8$

Put it in $\left(1\right)⟹(8t+8)\left(t\right)=240t^2+t-30=0t^2+6t-5t-30=0t(t+6)-5(t+6)=0(t-5)(t+6)=0t=5,-6$

Time cannot be negative so $t=5$

Put it in $\left(1\right)$

$⟹x\left(5\right)=240⟹x=12kmph$