Question

Из пункта А в пункт В выехал грузовик. Через 1 час также из А в В выехала легковая машина, прибывшая в пункт В одновременно с грузовиком. Если бы автомобили выехали из пунктов А и А одновременно навстречу друг другу, то они встретились бы через 1 час 12 мин. Сколько времени провела в пути каждая машина?

Answer 1

За 1 примем расстояние между пунктами. Тогда автомобиль проходит его на час быстрее чем грузовик, а одновременно они его проходят за 1,2 часа. Имеем систему уравнений:
1/V1-1/V2=1,
(V1+V2)×1,2=1;
V2-V1=V1×V2,
V1+V2=10/12;
Рассмотрим второе уравнение системы V1=10/12-V2
V2-10/12+V2=10/12V2-V2²
V2=x
2x-10/12-10/12x+x²=0
x²+14/12x-10/12=0
12x²+14x-10=0
6x²+7x-5=0
D=49+120=169=13²
x1=(-7+13)/12=6/12=0,5
x2=(-7-13)/12=-20/12=-10/6 <0 - не соответствует условию
Скорость автомобиля 0,5, тогда скорость грузовика 10/12-6/12=4/12=⅓. Тогда автомобиль потратит на всё расстояние 1:0,5=2 часа, а грузовик 1:⅓=3 часа.

Answer 2

Problem Analysis

We have a scenario where a truck and a car travel from point A to point B. The car departs 1 hour after the truck and arrives at point B at the same time as the truck. If the vehicles had departed from points A and A simultaneously, they would have met after 1 hour and 12 minutes. We need to determine the travel time for each vehicle.

Solution

Let's assume the travel time for the truck is T hours and the travel time for the car is C hours.

We know that the car departs 1 hour after the truck and arrives at point B at the same time as the truck. This means that the car's travel time is equal to the truck's travel time plus 1 hour.

So, we can write the following equation: C = T + 1

We also know that if the vehicles had departed from points A and A simultaneously, they would have met after 1 hour and 12 minutes. This means that the total travel time for both vehicles is 1 hour and 12 minutes.

Converting 1 hour and 12 minutes to hours, we get: 1 hour and 12 minutes = 1 + 12/60 = 1.2 hours

So, we can write the following equation: T + C = 1.2

Now, we have a system of two equations with two variables. We can solve this system to find the values of T and C.

Solving the System of Equations

Substituting the value of C from the first equation into the second equation, we get: T + (T + 1) = 1.2

Simplifying the equation, we have: 2T + 1 = 1.2

Subtracting 1 from both sides of the equation, we get: 2T = 0.2

Dividing both sides of the equation by 2, we get: T = 0.1

Substituting the value of T into the first equation, we get: C = 0.1 + 1 = 1.1

Answer

Therefore, the truck spent 0.1 hours (or 6 minutes) on the road, and the car spent 1.1 hours (or 1 hour and 6 minutes) on the road.

Please note that these calculations are based on the given information and assumptions made.