# From city A to city B located at a distance of 360 km, two cars left. The speed of one is 80 km / h more than the speed of the other

From city A to city B located at a distance of 360 km, two cars left. The speed of one is 80 km / h more than the speed of the other, so he arrived 6 hours earlier. Find the speed of each car.

Let’s write an equation in which we write the speed of the first car as x km / h.
Since the speed of the second car is 80 km / h higher, its speed will be: x + 80 km / h.
The ratio of distance traveled to speed is time, so we get the following difference equation:
360 / x – 360 / (x + 80) = 6.
360 * (x + 80) – 360 * x = 6 * (x2 + 80 * x).
360 * x + 28800 – 360 * x = 6 * x2 + 480 * x.
6 * x2 + 480 * x – 28800 = 0.
x2 + 80 * x – 4800 = 0.
√D = 802 – 4 * 1 * (-4800) = 6400 + 19200 = 25600.
D = √25600 = 160.
x = (-80 + 160) / 2 = 80/2 = 40 km / h (speed of the first car).
x + 80 = 40 + 80 = 120 km / h (second speed).
Answer: 40 and 120 km / h.

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