Question

Из А в В одновременно выехали два автомобилистов . первый проехал с постоянной скоростью весь путь . Второй проехал первую половину пути со скоростью 55 км\ч,а вторую половину пути со скоростью на 6км\ч больше скорости первого,в результате чего прибыл в В одновременно с первым автомобилистов. Найдите скорость первого автомобилиста.

Answer 1

Решение:
Обозначим скорость первого автомобилиста за (х) км/час, а полный путь автомобилиста за единицу (1) пути, тогда время в пути первого автомобилиста составило:
1/х (час)
Второй автомобилист проехал первую половину пути за (1/2:55) часа,
вторую половину пути второй автомобилист двигался со скоростью (х+6) км/час и проехал вторую половину пути за {1/2:(х+6)} часа
А так как автомобилисты приехали в город В одновременно, то есть потратили одинаковое количество времени в пути, составим уравнение:
1/х=(1/2:55)+{1/2:(х+6)}
1/х=1/110+1/(2х+12)
110*(2х+12)=х*(2х+12)*1+х*110*1
220х+1320=2x^2+12x+110x
2x^2+12x+110x-220x-1320=0
2x^2-98x-1320=0
x1,2=(98+-D)/2*2
D=√(9604-4*2*-1320)=√(9604+10560)=√20164=142
х1,2=(98+-142)/4
х1=(98+142)/4=240/4=60 (км/час) - скорость первого автомобилиста
х2=(98-142)/4=-44/4=11 - не соответствует условию задачи

Ответ: Скорость первого автомобилиста равна 60 км/час

Answer 2

Problem Analysis

We are given that two drivers, A and B, simultaneously traveled 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 of 55 km/h and the second half at a speed 6 km/h faster than driver A. We need to find the speed of driver A.

Solution

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

Driver A traveled the entire distance at a constant speed, so the time taken by driver A is given by: Time taken by A = D / Speed of A Driver B traveled the first half of the distance at a speed of 55 km/h, so the time taken by driver B for the first half is given by: Time taken by B for first half = (D/2) / 55 Driver B traveled the second half of the distance at a speed 6 km/h faster than driver A, so the time taken by driver B for the second half is given by: Time taken by B for second half = (D/2) / (Speed of A + 6) Since both drivers arrived at point B simultaneously, the total time taken by driver A and driver B should be the same. Therefore, we can equate the time taken by driver A and the total time taken by driver B:

D / Speed of A = (D/2) / 55 + (D/2) / (Speed of A + 6)

To solve for the speed of driver A, we can rearrange the equation:

D / Speed of A = (D/2) / 55 + (D/2) / (Speed of A + 6)

D / Speed of A = D / (2 * 55) + D / (2 * (Speed of A + 6))

Multiplying both sides of the equation by Speed of A * (2 * 55) * (2 * (Speed of A + 6)), we get:

D * (2 * 55) * (2 * (Speed of A + 6)) = D * Speed of A * (2 * (Speed of A + 6)) + D * (2 * 55) * Speed of A

Simplifying the equation, we have:

Speed of A * (2 * 55) * (2 * (Speed of A + 6)) = Speed of A * (2 * (Speed of A + 6)) + (2 * 55) * Speed of A

Simplifying further, we get:

Speed of A * (2 * 55) * (2 * Speed of A + 12) = Speed of A * (2 * Speed of A + 12) + (2 * 55) * Speed of A

Expanding and simplifying, we have:

Speed of A * (220 * Speed of A + 1320) = Speed of A * (4 * Speed of A + 24) + 110 * Speed of A

Simplifying further, we get:

220 * Speed of A^2 + 1320 * Speed of A = 4 * Speed of A^2 + 24 * Speed of A + 110 * Speed of A

Combining like terms, we have:

216 * Speed of A^2 - 106 * Speed of A - 24 * Speed of A = 0

Simplifying further, we get:

216 * Speed of A^2 - 130 * Speed of A = 0

Factoring out Speed of A, we have:

Speed of A * (216 * Speed of A - 130) = 0

Setting each factor equal to zero, we have:

Speed of A = 0 or Speed of A = 130 / 216

Since the speed of a car cannot be zero, the speed of driver A is:

Speed of A = 130 / 216 km/h

Therefore, the speed of the first driver is 130 / 216 km/h.

Answer

The speed of the first driver is 130 / 216 km/h.