Two motorists left A and B at the same time. The first drove at a constant speed all the way.

| May 3, 2021 | education

Two motorists left A and B at the same time. The first drove at a constant speed all the way. The second traveled the first half of the journey with a mow of 30 km / h, and the second half of the journey traveled at a speed of 9 km / h more than the speed of the first, as a result of which he arrived in B simultaneously with the first motorist. Find the speed of the first motorist.

1. Let’s denote the speed of the first motorist through X, and the distance between points A and B via L.

2. Then the time T1, which took the first motorist to travel from A to B, defined by the expression: T1 = L / X.

3. The time T2 of the second motorist on the way from A to B is determined by the expression:
T2 = (L / 2) / 30 + (L / 2) / (X + 9).

4. By the condition of the problem, T1 = T2. We get the equation: (L / 2) / 30 + (L / 2) / (X + 9) = L / X.

5. Perform the following actions with the equation: divide both sides of the equation by L, multiply both sides of the equation by [2 * 30 * X * (X + 9)]. We get a quadratic equation:
X ^ 2 – 21 * X – 540 = 0.

6. The discriminant of the equation D ^ 2 = 441 + 2160 = 2601. Or D = 51.

7. The roots of the equation X = 36 and X = – 15. The negative root does not satisfy the condition of the problem.

Answer: the speed of the first motorist is 36 km / h.



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