From point A to point B, the car drove along a highway with a length of 210 km, and returned from B to A along a dirt road with a length of 160 km, spending 1 hour more on the way back than on the way from A to B. Find the speed at which it was driving a car on a dirt road if it is 30 km / h less than its speed on a highway.
Suppose that a car was driving on a dirt road at a speed of x km / h, then on a highway it was driving at a speed of x + 30 km / h.
According to the condition of the problem, we compose and solve the equation:
210 / (x + 30) = 160 / x – 1,
210 / (x + 30) = (160 – x) / x,
210 * x = 160 * x – x² + 4800 – 30 * x,
-x² – 80 * x + 4800 = 0.
The discriminant of this quadratic equation is:
(-80) ² – 4 * (-1) * 4800 = 25600.
Since x can only be a positive number, the problem has a unique solution:
x = (80 – 160) / – 2 = 80 (km / h) – vehicle speed on a dirt road.
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