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.

Let the speed of car be x km/h

Given, if speed been 12 km/h more, the time taken for the journey would have been 1 hour 40 minutes less

1 hour 40 minutes = $\dfrac{100}{60}$ hours

Since, Time = $\dfrac{\text{Distance}}{\text{Speed}}$

$\therefore \dfrac{400}{x} - \dfrac{400}{x + 12} = \dfrac{100}{60} \\[1em] \Rightarrow 100(\dfrac{4}{x} - \dfrac{4}{x + 12}) = \dfrac{100}{60} \\[1em] \Rightarrow \dfrac{4}{x} - \dfrac{4}{x + 12} = \dfrac{1}{60} \\[1em] \Rightarrow \dfrac{4(x + 12) - 4x}{x(x + 12)} = \dfrac{1}{60} \\[1em] \Rightarrow 60(4x + 48 - 4x) = x(x + 12) \\[1em] \Rightarrow 60 \times 48 = x^2 + 12x \\[1em] \Rightarrow x^2 + 12x - 2880 = 0 \\[1em] \Rightarrow x^2 + 60x - 48x - 2880 = 0 \\[1em] \Rightarrow x(x + 60) - 48(x + 60) = 0 \\[1em] \Rightarrow (x - 48)(x + 60) = 0 \\[1em] \Rightarrow x - 48 = 0 \text{ or } x + 60 = 0 \\[1em] x = 48 \text{ or } x = -60$

Since speed of train cannot be negative hence, x ≠ -60

Hence, the speed of express train is 48 km/h.