A bus left the village for the city. After 1 hour, a passenger car drove out to meet him from the city to the village, the speed of which is 20 kh / h more than the speed of the bus. They met in the middle of the road connecting the village and the city. Find the speed of a car if the distance from the village to the city is 480 km.
Let’s denote the speed of the bus by x km / h (x ›0), the speed of the car (x + 20) km / h.
They met in the middle of the road.
The bus traveled 240 / x (h), and the car traveled 240 / (x + 20) (h).
We know that the car spent 1 hour less.
We compose and solve the equation.
240 / x – 240 / (x + 20) = 1,
240 * (x + 20) – 240x = x * (x + 20),
x2 + 20x – 4800 = 0.
By a theorem converse to Vieta’s theorem, we find the roots.
x1 = -80 – not suitable,
x2 = 60 (km / h) – bus speed.
60 + 20 = 80 (km / h) – vehicle speed.
Answer: 80 km / h.
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