Question

Из 2 поселков одновременно навстречу друг другу выехали два автомобиля. Один скоростью 106 км ч и проехал до встречи 424 км. Опередили расстояние между посёлками, скорость второго автомобиля 98 км ч.

Answer 1

424 : 106 = 4 (ч) - время в пути.
98 • 4 = 392 (км) - проехал второй автомобиль.
424 + 392 = 816 (км) - расстояние между поселками.
Ответ: 816 км.

Answer 2

Problem Analysis

We are given that two cars start simultaneously from two different villages and are driving towards each other. The first car is traveling at a speed of 106 km/h and has traveled 424 km until they meet. We need to find the distance between the villages and the speed of the second car, which is traveling at 98 km/h.

Solution

Let's denote the distance between the villages as d and the speed of the second car as v.

We know that the first car has traveled 424 km until they meet. Since the two cars are driving towards each other, the sum of the distances traveled by both cars should be equal to the distance between the villages:

424 km + v * t = d (Equation 1)

where t is the time it takes for the two cars to meet.

We also know that the first car is traveling at a speed of 106 km/h, so we can calculate the time it takes for the first car to meet the second car:

t = 424 km / 106 km/h = 4 hours (Equation 2)

Substituting Equation 2 into Equation 1, we can solve for d:

424 km + v * 4 hours = d

Simplifying the equation:

d = 424 km + 4v (Equation 3)

Now, we can substitute the given speed of the second car (98 km/h) into Equation 3 to find the distance between the villages:

d = 424 km + 4 * 98 km/h

Calculating the value:

d = 424 km + 392 km = 816 km

Therefore, the distance between the villages is 816 km and the speed of the second car is 98 km/h.

Answer

The distance between the two villages is 816 km and the speed of the second car is 98 km/h.