Question

Первые 200 км дороги из А в B автомобиль проехал с определенной скоростью, а остальные 150 км – со скоростью на 20 км/ч меньшей. Найти начальную скорость, с которой ехал автомобиль, если на весь путь из А в B он затратил 5 ч. ​

Answer 1

Ответ:

пусть х-начальная скорость

200:х+150(х-20)=5

40(х-20)+30х=х(х-20)

40х-800+30х=х*х-20х

х*х-90х+800=0

D=70

x=(90+-70)/2

x=10 такого не может быть,т.к. он уменьшал скорость на 20

х=80км:ч

Объяснение:

Answer 2

Problem Analysis

We are given that a car traveled the first 200 km of a road from point A to point B at a certain speed, and then traveled the remaining 150 km at a speed 20 km/h slower. We need to find the initial speed of the car if the total time taken for the entire journey from A to B was 5 hours.

Solution

Let's assume the initial speed of the car is v km/h.

The time taken to travel the first 200 km at speed v is given by: t1 = 200/v (Equation 1)

The time taken to travel the remaining 150 km at a speed 20 km/h slower is given by: t2 = 150/(v-20) (Equation 2)

The total time taken for the entire journey is given as 5 hours: t1 + t2 = 5 (Equation 3)

We can now solve these equations to find the value of v.

Calculation

Let's substitute the values from Equations 1 and 2 into Equation 3 and solve for v:

200/v + 150/(v-20) = 5

Multiplying through by v(v-20) to eliminate the denominators:

200(v-20) + 150v = 5v(v-20)

Expanding and simplifying:

200v - 4000 + 150v = 5v^2 - 100v

Rearranging and simplifying:

5v^2 - 450v + 4000 = 0

Using the quadratic formula to solve for v:

v = (-b ± sqrt(b^2 - 4ac)) / (2a)

where a = 5, b = -450, and c = 4000.

Substituting the values:

v = (-(-450) ± sqrt((-450)^2 - 4 * 5 * 4000)) / (2 * 5)

Simplifying:

v = (450 ± sqrt(202500 - 80000)) / 10

v = (450 ± sqrt(122500)) / 10

v = (450 ± 350) / 10

So, the possible values for v are:

v1 = (450 + 350) / 10 = 80 km/h

v2 = (450 - 350) / 10 = 10 km/h

However, since the car traveled the first 200 km at a certain speed, it is reasonable to assume that the initial speed of the car was 80 km/h.

Answer

The initial speed with which the car traveled from point A to point B was 80 km/h.