Question

Из села в город выехала легковая машина через 2 часа и оставалось проехать Расстояние которое в 4 раза меньше пройденного пути Чему равно расстояние от села до города если скорость легковой машины равна 8 километров в час Реши задачу разными способами

Answer 1

11.5*2.4=27.6км - успел проехать велосипедист46-11,5=34,5км/ч - скорость сближения27,6:34,5=0,8ч - мотоциклись догнал велосипедиста46*0,8=36,8км - проехал мотоциклист40*36,8=3,2км - расстояние до города Ответ: через 0,8 часов они встетились на расстоянии 3,2 км от города. 

Answer 2

Problem Analysis

We are given that a car traveled from a village to a city. After 2 hours of travel, the remaining distance to be covered is 4 times smaller than the distance already traveled. We are also given that the speed of the car is 8 kilometers per hour. We need to find the distance from the village to the city.

Solution 1: Using Algebra

Let's assume the total distance from the village to the city is D kilometers. According to the problem, after 2 hours of travel, the remaining distance is 4 times smaller than the distance already traveled. This means that after 2 hours, the car has traveled D - (D/4) = 3D/4 kilometers.

We can set up the following equation to solve for D: D - (3D/4) = 2 * 8

Simplifying the equation: 4D - 3D = 16 D = 16

Therefore, the distance from the village to the city is 16 kilometers.

Solution 2: Using Proportions

Another way to solve this problem is by setting up a proportion. We know that the remaining distance is 4 times smaller than the distance already traveled. Let's represent the distance already traveled as x kilometers. The remaining distance would then be x/4 kilometers.

We can set up the following proportion: x/4 = 2 * 8/x

Cross-multiplying and simplifying the equation: x^2 = 64 x = √64 x = 8

Therefore, the distance already traveled is 8 kilometers. Since the remaining distance is 4 times smaller, the total distance from the village to the city is 4 * 8 = 32 kilometers.

Conclusion

Using either algebra or proportions, we can determine that the distance from the village to the city is 16 kilometers or 32 kilometers.