Question

Из А в В одновременно выехали два автомобилиста. Первый проехал с постоянной скоростью весь путь. Второй проехал первую половину пути со скоростью, меньшей скорости первого на 10 км/ч, а вторую половину пути — со скоростью 84 км/ч, в результате чего прибыл в В одновременно с первым автомобилистом. Найдите скорость первого автомобилиста, если известно, что она больше 40 км/ч. Ответ дайте в км/ч.

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given that two drivers, A and B, simultaneously started their journey from point A to point B. Driver A traveled the entire distance at a constant speed, while driver B traveled the first half of the distance at a speed 10 km/h slower than driver A and the second half at a speed of 84 km/h. We need to find the speed of driver A, knowing that it is greater than 40 km/h.

Solution

Let's assume the total distance from point A to point B is d km.

We can use the formula speed = distance / time to find the time taken by each driver to travel the distance.

For driver A, the speed is denoted by v km/h, and the time taken is t1 hours. Therefore, we have:

v = d / t1 (Equation 1)

For driver B, the first half of the distance is d/2 km, and the speed is v - 10 km/h. The time taken to cover the first half is t2 hours. The second half of the distance is also d/2 km, and the speed is 84 km/h. The time taken to cover the second half is t3 hours. Therefore, we have:

d/2 = (v - 10) * t2 (Equation 2)

d/2 = 84 * t3 (Equation 3)

Since both drivers arrived at point B simultaneously, the total time taken by driver A should be equal to the total time taken by driver B. Therefore, we have:

t1 = t2 + t3 (Equation 4)

We can solve this system of equations to find the value of v.

Solution Steps

1. Substitute the values from Equation 2 and Equation 3 into Equation 4 to eliminate t2 and t3. 2. Simplify the equation to solve for t1. 3. Substitute the value of t1 into Equation 1 to find the value of v.

Let's solve the equations step by step:

Step 1:

Substituting the values from Equation 2 and Equation 3 into Equation 4, we get:

(d/2) / (v - 10) = d/2 / 84 + d/2 / v (Equation 5)

Step 2:

Simplifying Equation 5, we get:

1 / (v - 10) = 1 / 84 + 1 / v (Equation 6)

Step 3:

Substituting the value of t1 into Equation 1, we get:

v = d / (d / (v - 10)) (Equation 7)

Simplifying Equation 7, we get:

v = (v - 10) (Equation 8)

Solving Equation 8 for v, we find:

v = 10 km/h

Therefore, the speed of the first driver, driver A, is 10 km/h.

Answer

The speed of the first driver, driver A, is 10 km/h.