# From city A to city B, the distance between which is 210 km, two cars left at the same time.

From city A to city B, the distance between which is 210 km, two cars left at the same time. The speed of one of them is 10 km / h more than the speed of the other, thanks to which he arrived in city B 30 minutes faster. Find the speed of each car.

To solve the problem, let’s write an equation in which the speed of the first car is written as x km / h.

In this case, the speed of the second car will be:

x + 10 km / h.

Spent the first car all the way:

210 / h.

The second car was spent all the way:

210 / (x + 10).

The time difference will be 30 minutes.

30 minutes = 0.5 hours.

210 / x – 210 / (x + 10) = 0.5.

210 * (x + 10) – 210 * x = 0.5 * x * (x + 10).

210 * x + 2100 – 210 * x = 0.5 * x ^ 2 + 5 * x.

0.5 * x ^ 2 + 5 * x – 2100 = 0.

D ^ 2 = 25 – 4 * 0.5 * (-2100) = 25 + 4200 = 4225.

D = 65.

x = (-5 + 65) / 2 = 30 km / h (speed of the first car).

x + 10 = 3 + 10 = 40 km / h (speed of the second car).

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