Question

Из А в В одновременно выехали два автомобиля. Первый проехал с постоянной скоростью весь путь.Второй проехал первую половину пути со скоростью, меньшей скорости первого на 16 км/ч, а вторую половину пути - со скоростью 96 км/ч, в результате чего прибыл в В одновременно с первым автомобилем. Найдите скорость первого автомобиля, если известно, что она больше 60 км/ч.

Answer 1

Пусть скорость первого  равна х км/час , тогда второй S/2 пути  х-16 км/час ,  слудующую   S/2  км  оон проезал со  скоростью  96 км/час,  время у них одинаковые 
t1 = S/x t2 = (S/2)/(x-16) + (S/2)/96
t1=t2
S/x= (S/2)/(x-16) + (S/2)/96  S/x=  S/(2x-32) + S/192 
сократим  S
1/x = 1/(2x-32) + 1/192
(2x-32)192 = 192x +x(2x-32)
384x-6144=192x+2x^2-32x
2x^2-224x+6144=0
(x-48)(x-64)=0
x=48x=64
По условию  64>60  ответ   64км/час 

Answer 2

Problem Analysis

We are given that two cars, A and B, simultaneously started from point A and traveled to point B. The first car traveled the entire distance at a constant speed. The second car traveled the first half of the distance at a speed 16 km/h slower than the first car and the second half of the distance at a speed of 96 km/h. We need to find the speed of the first car, given that it is greater than 60 km/h.

Solution

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

The first car traveled the entire distance at a constant speed, which we'll call v km/h.

The second car traveled the first half of the distance at a speed 16 km/h slower than the first car, so its speed for the first half of the distance is v - 16 km/h.

The second car traveled the second half of the distance at a speed of 96 km/h.

To find the time taken by each car, we can use the formula:

time = distance / speed

For the first car, the time taken is:

time1 = d / v

For the second car, the time taken for the first half of the distance is:

time2_1 = (d / 2) / (v - 16)

And the time taken for the second half of the distance is:

time2_2 = (d / 2) / 96

Since both cars arrived at point B simultaneously, the total time taken by each car should be the same:

time1 = time2_1 + time2_2

Substituting the values, we get:

d / v = (d / 2) / (v - 16) + (d / 2) / 96

Simplifying the equation, we get:

d / v = d / (2(v - 16)) + d / (2 * 96)

Multiplying through by the common denominator, we get:

96d = d(v - 16) + v(d / 2)

Simplifying further, we get:

96d = dv - 16d + vd / 2

Combining like terms, we get:

96d = dv + vd / 2 - 16d

Multiplying through by 2 to eliminate the fraction, we get:

192d = 2dv + vd - 32d

Rearranging the terms, we get:

192d - 32d = 2dv + vd

Simplifying further, we get:

160d = 3dv

Dividing both sides by 3d, we get:

160 / 3 = v

Therefore, the speed of the first car, v, is equal to 160 / 3 km/h.

Answer

The speed of the first car is 160 / 3 km/h, which is approximately 53.33 km/h.