From city A to city B, the distance between which is 400 km, a bus left. An hour later, a passenger car drove out after him, the speed of which is 20 km / h more than the speed of the bus. They left for city B at the same time. Find the bus speed.
1. Let’s denote the speed of the bus as x km / h.
2. In one hour, the bus traveled x km, and it remains to go to point B (400 – x) km.
3. The speed of the car will be (x + 20) km / h.
4. The time it takes for the bus to travel the remaining path is equal to the time it takes for the car to travel from A to B:
(400 – x) / x = 400 / (x + 20);
(400 – x) * (x + 20) = 400 * x.
5. Expand the brackets:
400 * x + 8000 – x² – 20 * x = 400 * x.
x² + 20 * x – 8000 = 0
6. By Vieta’s theorem, the roots are equal:
x = -100 <0, x = 80.
Answer: the bus speed is 80 km / h.
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