Question

Два автомобиля одновременно въехали навстречу друг другу из городов,находящихся на расстоянии 510 км. Скорость первого автомобиля составляет 70% скорости второго. Через сколько часов автомобили встретятся,если скорость второго больше скорости первого на 30 км/ч?

Answer 1

Пусть Х1 и Х2 скорости автомобилей, по условиям задачи для них справедливы соотношения:

Х1 = 0,7*Х2
Х2 - Х1 = 30

решим систему уравнений подстановкой и определим скорости :

Х2 - 0,7*Х2 = 30    0,3*Х2 = 30   Х2 = 30/0,3 = 100
Х1=0,7*Х2 = 0,7*100 = 70

Двигаясь навстречу друг другу машины сближаются со соростью равной

70+100 = 170 км/ч

на дистанции 510 км встреча произойдёт через

510/170 = 3 часа

Answer 2

Problem Analysis

Two cars are traveling towards each other from cities that are 510 km apart. The speed of the first car is 70% of the speed of the second car, and the second car is 30 km/h faster than the first. We need to find out how many hours it will take for the cars to meet.

Calculating the Time of Meeting

Let's denote the speed of the first car as v km/h and the speed of the second car as v + 30 km/h. We can use the formula distance = speed × time to calculate the time it takes for the cars to meet.

The total distance traveled by both cars when they meet is 510 km. We can set up the following equation to solve for the time it takes for the cars to meet:

70% of v + (v + 30) = 510

Solving this equation will give us the value of v, and then we can calculate the time it takes for the cars to meet.

Calculation

Let's solve the equation to find the value of v:

0.7v + v + 30 = 510

1.7v = 480

v = 282.35

Now, we can calculate the time it takes for the cars to meet using the formula time = distance / speed.

The time it takes for the cars to meet is:

time = 510 / (0.7v + v + 30)

Result

The time it takes for the cars to meet is approximately 1.5 hours.