Question

Мотоциклист задержался у шлагбаума на 24 мин. Увеличив после этого скорость на 10 км\ч, он наверстал опоздание за 80 км. Определите первоначальную скорость мотоциклиста.

Answer 1

24 мин=0,4 часа

Составим уравнение 80/(V+10)+0.4=80/V

Приведя к общему знаменателю, получим 80V+800=80V+0.4V^2+4V,

0,4V^2+4V-800=0   D=4^2+4*0.4*800=1296   Корень из D=36   V=(-4+36)/2*0.4=40 км/ч.

Answer 2

Problem Analysis

We are given that a motorcyclist was delayed at a barrier for 24 minutes. After this delay, the motorcyclist increased their speed by 10 km/h and made up for the delay by traveling an additional 80 km. We need to determine the motorcyclist's initial speed.

Solution

Let's assume the motorcyclist's initial speed is x km/h.

1. The motorcyclist was delayed for 24 minutes, which is equivalent to 24/60 = 0.4 hours. 2. After the delay, the motorcyclist increased their speed by 10 km/h, so their new speed is (x + 10) km/h. 3. The motorcyclist made up for the delay by traveling an additional 80 km. 4. We can set up the following equation to represent the situation: (x + 10) * t = x * (t + 0.4) + 80 where t represents the time taken to travel the additional 80 km. 5. Simplifying the equation: xt + 10t = xt + 0.4x + 80 10t - 0.4x = 80 6. Rearranging the equation: 10t = 0.4x + 80 t = (0.4x + 80) / 10 7. Substituting the value of t in the equation: (x + 10) * [(0.4x + 80) / 10] = x * [(0.4x + 80) / 10] + 80 8. Simplifying the equation: (x + 10) * (0.4x + 80) = x * (0.4x + 80) + 800 0.4x^2 + 8x + 800 = 0.4x^2 + 8x + 800 9. The equation simplifies to: 0 = 0 10. Since the equation simplifies to 0 = 0, it means that any value of x will satisfy the equation. 11. Therefore, the initial speed of the motorcyclist can be any value.

Answer

The initial speed of the motorcyclist can be any value.