The first skier is 20 km faster than the second skier by 20 minutes. Determine the speed of the second skier if it is known

| January 6, 2021 | education

The first skier is 20 km faster than the second skier by 20 minutes. Determine the speed of the second skier if it is known that it is 2 km / h less than the speed of the first skier. Let x km / h be the speed of the second skier. What equation does not correspond to the condition of the problem?

Let’s take the speed of the second skier as x, then:
x + 2 – speed of the first;
20: x = 20 / x – movement time of the second;
20: (x + 2) = 20 / (x + 2) – time of the first.
Since the time difference is 20 minutes = 1/3 hour, we get the equation:
20 / x – 20 / (x + 2) = 1/3.
20x + 40 – 20x = 1 / 3x (x + 2);
x ^ 2 + 2x – 120 = 0.
x12 = (-2 + – √ (4 – 4 * 1 * (-120)) / 2 * 1 = (-2 + – 22) / 2;
x1 = (-2 – 22) / 2 – has no physical meaning.
x2 = (-2 + 22) / 2 = 10.
Answer: the speed of the second skier is 10 km / h.



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