Question

A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
[4 MARKS]

Answer 1

Framing the equation: 1 Mark
Steps: 2 Marks
Answer: 1 Mark

Let the original speed be x.
Then $T_1=\frac{400}{x}...\left(i\right)$
If speed =x+12, $T_2=\frac{400}{x+12}...\left(ii\right)$
But $T_1-T_2=1\frac{40}{60}$
$\Rightarrow \frac{400}{x}-\frac{400}{x+12}=\frac{5}{3}\Rightarrow 5x^2+60x-14400=0\Rightarrow x^2+12x-2880=0\Rightarrow x^2+60x-48x-2880=0\Rightarrow (x-48)(x+60)=0$
$\Rightarrow x=48;x=-60$(Not possible)
$\therefore$ Original speed of car is 48 km/h