Question

РЕшиет плизиз пункта А в пункт В одновременно выехали два автомобиля , один со скоростью 60 км / ч , второй со скоростью 70 км/ч . через полчаса вслед за ними выехал мотоциклист со скоростью x км /ч который через некоторое время обогнал оба автомобиля1) ЗАПИШИТЕ В ВИДЕ ВЫРАЖЕНИЯ- скорость сближения мотоциклиста и первого автомобиля-скорость сближения мотоциклиста и второго автомобиля2)НАЙДИТЕ НЕОБХОДИМЫЕ ВЕЛИЧИНЫ И ЗАПИШИТЕ ОТВЕТ В ВИДЕ ВЫРАЖЕНИЯ-сколько времени потребовалось мотоциклисту чтобы догнать первый автомобиль-сколько времени потребуется мотоциклисту чтобы догнать второй автомобиль-сколько времени прошло с момента обгона первого автомобиля до момента обгона второго3) ЗАПИШИТЕ ТРЕМЯ СПОСОБАМИ В ВИДЕ РАВЕНСТВАУСЛОВИЕ : мотоциклист обогнал второй автомобиль через 1 час 30 минут после того как обогнал первый

Answer 1

расстояние АВ= S

скорость первого мотоциклиста -v

время 1мотоц  t= S/v

Второй

 проехал первую половину пути со скоростью  v-20

за время t1=(S/2)/(v-20)

вторую половину пути со скоростью 126 км/ч

за время t2=(S/2)/126

t=t1+t2

S/v=(S/2)/(v-20) +(S/2)/126

1/v=1/(2*(v-20)) +1/252

1/v-1/252=1/(2*(v-20))

(252-v)/252v= 1/(2*(v-20))

(252-v)(2*(v-20))=252v

(252-v)(v-20)=126v

v^2-146v+5040

после решения квадратного уравнения

v = 56   или v=90

по условию скорость больше 60 км/ч.

 

Ответ скорость первого мотоциклиста 90 км/ч.

Answer 2

Given Information:

Two cars simultaneously set off, one with a speed of 60 km/h and the other with a speed of 70 km/h. After half an hour, a motorcyclist sets off with a speed of x km/h and eventually overtakes both cars. The following questions need to be answered:

1. Speed of Approach: - Write the expressions for the speed of approach between the motorcyclist and the first car, and between the motorcyclist and the second car.

2. Time to Overtake: - Find the time it took for the motorcyclist to overtake the first car. - Find the time it will take for the motorcyclist to overtake the second car.

3. Time Between Overtakes: - Find the time that passed between the motorcyclist overtaking the first car and overtaking the second car.

4. Three Equations: - Write three equations based on the given condition: the motorcyclist overtakes the second car 1 hour and 30 minutes after overtaking the first car.

Speed of Approach:

The speed of approach between two moving objects is the relative speed at which they are getting closer to each other. In this case, we need to find the speed of approach between the motorcyclist and each car.

Let's denote the speed of the motorcyclist as v km/h.

The speed of approach between the motorcyclist and the first car is the difference between their speeds: Speed of approach between motorcyclist and first car = v - 60 km/h.

The speed of approach between the motorcyclist and the second car is also the difference between their speeds: Speed of approach between motorcyclist and second car = v - 70 km/h.

Time to Overtake:

To find the time it took for the motorcyclist to overtake each car, we need to consider the distance traveled by each vehicle.

Let's assume the time taken by the motorcyclist to overtake the first car is t1 hours.

The distance traveled by the first car in t1 hours is 60 * t1 km.

The distance traveled by the motorcyclist in t1 hours is v * t1 km.

Since the motorcyclist overtakes the first car, the distances traveled by both vehicles must be equal: 60 * t1 = v * t1.

Simplifying the equation, we find: t1 = 60 / (v - 60).

Similarly, let's assume the time taken by the motorcyclist to overtake the second car is t2 hours.

The distance traveled by the second car in t2 hours is 70 * t2 km.

The distance traveled by the motorcyclist in t2 hours is v * t2 km.

Since the motorcyclist overtakes the second car, the distances traveled by both vehicles must be equal: 70 * t2 = v * t2.

Simplifying the equation, we find: t2 = 70 / (v - 70).

Time Between Overtakes:

To find the time that passed between the motorcyclist overtaking the first car and overtaking the second car, we need to subtract the time it took to overtake the first car from the time it took to overtake the second car.

Let's denote the time between overtakes as t3 hours.

The time it took to overtake the first car is t1 hours, and the time it took to overtake the second car is t2 hours.

Therefore, the time between overtakes is: t3 = t2 - t1.

Substituting the values of t1 and t2, we find: t3 = (70 / (v - 70)) - (60 / (v - 60)).

Three Equations:

Based on the given condition that the motorcyclist overtakes the second car 1 hour and 30 minutes after overtaking the first car, we can write three equations:

1. The time it took to overtake the first car is t1 hours: t1 = 60 / (v - 60).

2. The time it took to overtake the second car is t2 hours: t2 = 70 / (v - 70).

3. The time between overtakes is t3 hours: t3 = (70 / (v - 70)) - (60 / (v - 60)).

These equations can be used to solve for the value of v and find the answers to the given questions.

Please note that the search results provided by You.com did not provide specific information related to this problem. However, the solution provided above is based on the principles of relative motion and can be applied to solve the problem.