Question

1. Два автомобиля выехали одновременно из А в В, расстояние между которыми равно 420км. Скорость первого автомобиля на 20км/ч больше, поэтому он пришёл в В на 2ч 24мин раньше второго. Найти скорость каждого из них.

Answer 1

Пусть скорость одного автомобиля х км\час, тогда скорость другого х-20 км\час.
Составим уравнение:
420\(х-20) - 420\х = 2,4
420х-420(х-20)=2,4(х²-20х)
420х-420х+8400-2,4х²+48х=0
х²-20х-8400=0
х=70.
Скорость одного автомобиля 70 км\час, скорость другого 70-20=50 км\час.

Answer 2

Problem Analysis

We are given that two cars start simultaneously from point A and travel to point B, which is a distance of 420 km away. The first car travels at a speed that is 20 km/h faster than the second car. The first car arrives at point B 2 hours and 24 minutes earlier than the second car. We need to find the speed of each car.

Solution

Let's assume the speed of the second car is x km/h. Then, the speed of the first car is x + 20 km/h.

We can use the formula distance = speed × time to solve this problem.

The time taken by the first car to travel from A to B is given by (420 km) / (x + 20 km/h).

The time taken by the second car to travel from A to B is given by (420 km) / x km/h.

According to the problem, the first car arrives at point B 2 hours and 24 minutes earlier than the second car. This can be written as (2 hours + 24 minutes).

Converting 2 hours and 24 minutes to hours, we get (2 + 24/60) hours.

Now, we can set up the equation:

(420 km) / (x + 20 km/h) = (420 km) / x km/h + (2 + 24/60) hours

To solve this equation, we can cross-multiply and simplify:

(420 km) * x = (420 km) * (x + 20 km/h) + (2 + 24/60) hours * x * (x + 20 km/h)

Simplifying further:

(420 km) * x = (420 km) * x + (420 km) * 20 km/h + (2 + 24/60) hours * x^2 + (2 + 24/60) hours * 20 km/h * x

We can cancel out the common terms on both sides:

0 = (420 km) * 20 km/h + (2 + 24/60) hours * x^2 + (2 + 24/60) hours * 20 km/h * x

Simplifying further:

0 = (420 km) * 20 km/h + (2 + 24/60) hours * x^2 + (2 + 24/60) hours * 20 km/h * x

Now, we can solve this quadratic equation to find the value of x, which represents the speed of the second car.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = (2 + 24/60) hours * 20 km/h, b = (2 + 24/60) hours * 20 km/h, and c = -(420 km) * 20 km/h.

Plugging in the values, we get:

x = (-(2 + 24/60) hours * 20 km/h ± √((2 + 24/60) hours * 20 km/h)^2 - 4 * (2 + 24/60) hours * 20 km/h * (-(420 km) * 20 km/h)) / (2 * (2 + 24/60) hours * 20 km/h)

Simplifying further:

x = (-(2 + 24/60) hours * 20 km/h ± √((2 + 24/60) hours * 20 km/h)^2 + 4 * (2 + 24/60) hours * 20 km/h * (420 km) * 20 km/h) / (2 * (2 + 24/60) hours * 20 km/h)

Now, we can calculate the value of x using the quadratic formula.

Let's calculate the value of x:

x = 70 km/h or x = -80 km/h.

Since the speed cannot be negative, the speed of the second car is 70 km/h.

The speed of the first car is 70 km/h + 20 km/h = 90 km/h.

Therefore, the speed of the first car is 90 km/h and the speed of the second car is 70 km/h.

Answer

The speed of the first car is 90 km/h and the speed of the second car is 70 km/h.