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

Answer:

The answer will be 48km/hrs.

Step-by-step explanation:

Given things;

Distance = 400km

If speed = 12 km/hr more.

then time = 1 hour and 40 minutes less

Let the speed of the car be x.

Hence, time taken = 400/x;

So if speed would have been 12km/hr more which is;

(x + 12)km/hr;

then, time would have been;

(400/x) - 5/3; (1hr 40min in hours = 5/3 hours)

(1200 - 5x)/3x

Now, distance = speed × time;

Hence, 400 = (x +12)((1200 - 5x)/3x);

400 = (((x +12)1200 - (x +12)5x)/3x);

400 = ((1200x + 14400 - 5x^2 - 60x)/3x);

400 = ((1140x + 14400 - 5x^2)/3x);

1200x / 5 = 228x + 2880 - x^2;

240x = 228x + 2880 - x^2;

x^2 + 12x - 2880 = 0;

x^2 + (-48x) + (60)x - 2880 = 0;

x^2 - 48x + 60x - 2880 = 0;

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

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

Thus, x = -60. or,

x = 48

Since, speed could not be a negative integer, hence the original speed of the train will be 48km/hrs.

That's all.