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.

Answer 1

Hint: Use the information, Distance= time x speed. Let the initial speed and time be x and t respectively and create the first equation and with the second condition create a second equation and, in the end, solve them.

Complete step-by-step answer:

Let the speed of the car be x km/h and the time taken at that speed to cover 400 km be t minutes. Therefore, according to the first condition:
Distance=time x speed $ \Rightarrow 400 = xt \Rightarrow t = \dfrac{{400}}{x} - - - - (1)$
As per the second case, the distance remains the same, speed is increased to x+12 km/hr and the time reduces to t-100 minutes. So,
\[
   \Rightarrow 400 = (x + 12)(t - 100) \Rightarrow 400 = (x + 12)\left( {\dfrac{{400}}{x} - 100} \right) \Rightarrow 4 = (x + 12)\left( {\dfrac{4}{x} - 1} \right) \\
   \Rightarrow 4 = 4 - x + \dfrac{{48}}{x} - 12 \Rightarrow \dfrac{{48}}{x} - x = 12 \\
   \Rightarrow 48 - {x^2} = 12x \\
   \Rightarrow {x^2} + 12x - 48 = 0 \\
   \Rightarrow x = \dfrac{{ - 12 \pm \sqrt {{{( - 12)}^2} - 4( - 48)} }}{2} = \dfrac{{ - 12 \pm \sqrt {336} }}{2} = \dfrac{{ - 12 \pm 4\sqrt {21} }}{2} \\
   \Rightarrow x = - 6 + 2\sqrt {21} {\text{ or }}x = - 6 - 2\sqrt {21} \\
 \]
Since, the speed cannot be negative, we neglect the second answer. Hence, the original speed of the car is $2\sqrt {21} - 6 \approx 3.165$ km/hr.

Note: While solving, be careful with the calculation. Here we have neglected the negative numbers. It’s not true for all the questions. It's problem specific.