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 I hour 40 minutes less. Find the original speed of the car.

Answer 1

Let the original speed of the car be x kmph
case i:
Distance = 400 km
speed = x kmph
Time taken = hrs

case ii:
Distance = 400 km
speed = (x+12) kmph
Time taken=

But as per the question, the time taken is 1 hr 40 min lesser than the previous.

1 hr 40 min = 60+40 = 100min $\Rightarrow \frac{100}{60}=\frac{10}{6}=\frac{5}{3}$

that means,
ans,

$\frac{400}{x}-\frac{5}{3}=\frac{400}{x+12}$

$\frac{1200-5x}{3x}=\frac{400}{x+12}$

$1200x-5x^2+14400-60x=1200x$

$x^2+12x-2880=0$

(x - 48)(x + 60) = 0

x = 48 as the negative value of x is ignored.

The original speed of the car = 48 kmph