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.

Accepted Answer

Let $x km / h$ be the original speed of the car.

We know that,

$Time = \frac{Distance}{Speed}$

It is given that the car covers a distance of $400 km$ with the speed of $x km / h$ .

Thus, the time taken by the car to complete $400 km$ is

$t = \frac{400}{x}$

Now, the speed is increased by $12 km$ .

Increased speed $= (x + 12) km / h$

Also given that, increasing the speed of the car will decrease the time taken by $1$ hour $40$ minutes.

Hence,

$\frac{400}{x} - \frac{400}{x + 12} = 1$ hour $40$ minutes.

$\frac{400}{x} - \frac{400}{x + 12} = 1 \frac{40}{60}$

$\frac{400 (x + 12) - 400 x}{x (x + 12)} = 1 \frac{2}{3}$

$\frac{400 x + 4800 - 400 x}{x (x + 12)} = \frac{5}{3}$

$\frac{4800}{x (x + 12)} = \frac{5}{3}$

$3 \times 4800 = 5 \times x \times (x + 12)$

$14400 = 5 x^{2} + 60 x$

$5 x^{2} + 60 x - 14400 = 0$

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

$x^{2} + 60 x - 48 x - 2880 = 0$

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

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

$x + 60 = 0$ or $x - 48 = 0$

$x = - 60$ or $x = 48$

Since speed cannot be negative, the original speed of the car is $48 km / h$

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.

Important Questions on Solving (Simple) Problems (Based On Quadratic Equations)

Learn and Prepare for any exam you want !

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.

Important Questions on Solving (Simple) Problems (Based On Quadratic Equations)

Learn and Prepare for any exam you want !

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.