Question

Двое байкеров выехали одновременно из одного города в другой.Первый проехал путь со скоростью 96 км/ч .второй проехал первую половину пути со скоростью 80 км,ч. с какой скоростью пришлось ехать второму байкеру вторую половину пути ,если в другой город они приехали одновременно?ответ дайте в км.ч

Answer 1

Пусть Х---скорость первого байкера

тогда Х-16---скорость второго байкера на первой половине пути

путь они проехали один и тот же S

время потратили одинаковое:

время первого байкера S/X

время второго байкера S/(2*(X-16)) + S/(2*120)

получим уравнение

S/X = S/(2*(X-16)) + S/(2*120)

1/X = 1/(2*(X-16)) + 1/(2*120)

2/X - 1/(X-16) = 1/120

(2*(X-16) - Х) / (Х*(X-16)) = 1/120

120*(X-32) = Х*(X-16)

120*X - 120*32 - Х*X + 16*Х = 0

Х*X - 136*X + 120*32= 0

D = 136*136 - 4*120*32 = 8*17*8*17 - 4*2*60*8*4 = 8*8*(17*17 - 60*4) = 8*8*(289-240) = 8*8*49

X1 = (136 + 8*7)/2 = 68 + 4*7 = 96

X2 = (136 - 8*7)/2 = 68 - 4*7 = 40---не удовлетворяет условию

Ответ: скорость первого байкера 96 км/час

ПРОВЕРКА:

время в пути первого байкера S/96

время в пути второго байкера S/2 : (96-16) + S/2 : 120 = S/(2*80) + S/(2*120) = S/160 + S/240 = (3S+2S)/480 = 5S/480 = S/96

т.е. они доехали одновременно

Answer 2

Problem Setup

Two bikers set out from the same city to another city simultaneously. The first biker traveled at a speed of 96 km/h. The second biker covered the first half of the distance at a speed of 80 km/h. We need to find the speed at which the second biker had to travel for the second half of the distance to arrive at the other city at the same time as the first biker.

Solution

Let's denote the total distance between the two cities as D. Since both bikers arrived at the other city at the same time, we can use the formula: time = distance / speed.

The first biker's time to travel the distance D at a speed of 96 km/h is: time1 = D / 96.

The second biker's time to travel the first half of the distance at a speed of 80 km/h is: time2 = D / 2 / 80.

Since the second biker covered the first half of the distance at a speed of 80 km/h, the remaining distance to be covered is also D / 2.

Let's denote the speed at which the second biker had to travel for the second half of the distance as x km/h.

The second biker's time to travel the second half of the distance at a speed of x km/h is: time3 = D / 2 / x.

Since both bikers arrived at the other city at the same time, we have the equation: time1 = time2 + time3.

Substituting the expressions for time1, time2, and time3 into the equation, we can solve for x.

Calculation

Using the equation time1 = time2 + time3 and the given values: D / 96 = D / 2 / 80 + D / 2 / x.

Solving for x: D / 96 = D / 160 + D / 2x.

Multiplying through by 96x to clear the fractions: Dx = 96D + 48D.

Solving for x: x = 144D / D.

Result

The speed at which the second biker had to travel for the second half of the distance to arrive at the other city at the same time as the first biker is 144 km/h.