Question

СРОЧНО!!!!!Два автомобілі вирушають одночасно з одного міста в інше . Швидкість першого на 20 км/год більша ніж швидкість другого , тому він прибув на місце на 2 год 24 хв раніше ніж другий.З якою швидкістю їхав перший автомобіль якщо відстань між містами 420 км .

Answer 1

Хкм/ч-скорость первого
х-20)км/ч-скорость второго      2ч24мин=2ч+24/60=2+2/5=2,4
420/(х-20) -420/х=2,4
420х-420*(х-20)=12/5 *(x^2-20x)
12x^2-240x-420*5+420*(5x-100)=0
12x^2-240x+2100x-420*100-420*5=0
12x^2+1860x-420*105=0
x^2+155x-105*35=0
D=155^2+4*105*35=может ошибка где? Числа огромные! Или условие не так поняла!

Answer 2

Problem Analysis

We are given that two cars start simultaneously from one city to another. The first car's speed is 20 km/h faster than the second car, and it arrives at the destination 2 hours and 24 minutes earlier than the second car. We need to find the speed of the first car if the distance between the cities is 420 km.

Solution

Let's assume the speed of the second car is x km/h. Since the speed of the first car is 20 km/h faster, its speed will be x + 20 km/h.

We know that the time taken by the first car is 2 hours and 24 minutes (or 2.4 hours) less than the time taken by the second car. Let's convert this time difference to hours.

2 hours and 24 minutes = 2 + 24/60 = 2.4 hours

We can now set up an equation based on the given information:

Distance = Speed × Time

For the first car: Distance = 420 km Speed = x + 20 km/h Time = Time taken by the second car - 2.4 hours

For the second car: Distance = 420 km Speed = x km/h Time = Time taken by the second car

We can now write the equation:

420 = (x + 20) × (Time taken by the second car - 2.4)

Simplifying the equation:

420 = (x + 20) × (Time taken by the second car) - (x + 20) × 2.4

Now, let's solve this equation to find the value of x, which represents the speed of the second car.

Calculation

Let's solve the equation:

420 = (x + 20) × (Time taken by the second car) - (x + 20) × 2.4

We know that the distance between the cities is 420 km. Let's substitute this value into the equation:

420 = (x + 20) × (Time taken by the second car) - (x + 20) × 2.4

Simplifying further:

420 = (x + 20) × (Time taken by the second car) - 2.4x - 48

Now, let's solve for the time taken by the second car. We can rearrange the equation as follows:

420 + 48 = (x + 20) × (Time taken by the second car) - 2.4x

468 = (x + 20) × (Time taken by the second car) - 2.4x

Since we don't have the exact value of the time taken by the second car, we can't solve for the exact value of x. However, we can calculate the value of x in terms of the time taken by the second car.

Let's assume the time taken by the second car is t hours. Now we can rewrite the equation as:

468 = (x + 20) × t - 2.4x

Simplifying further:

468 = xt + 20t - 2.4x

Now, let's solve for x:

468 = xt - 2.4x + 20t

468 = x(t - 2.4) + 20t

x(t - 2.4) = 468 - 20t

x = (468 - 20t) / (t - 2.4)

So, the speed of the first car, represented by x, is given by (468 - 20t) / (t - 2.4) km/h.

Please note that we cannot determine the exact value of x without knowing