Question

Из села в направлении города выехал мотоциклист со скоростью 80 км/ч. через 1,5 чиз города в село выехал велосипедист со скоростью 16 км/ч. Сколько часов ехал до встречи каждый из них, если расстояние между городом и селом равно 216 км?Срочно помогите пожалуйста!!! Решите методом уравнения

Answer 1

1) 80км/ч*1,5ч=120км ( проехал мотоциклист , до выезда велосипедиста)
2)216км120км=96км ( остаток пути )
3) 80км/ч+16км/ч=96км/ч ( скорость сближения)
4) 96км:96км/ч =1час ( время остатка пути до встречи)
5)1,5ч+1ч=2,5ч ( время пути мотоциклиста)
6) 1ч ( время пути велосипедиста).

Answer 2

Problem Analysis

We are given that a motorcyclist travels from a village to a city at a speed of 80 km/h, and after 1.5 hours, a cyclist travels from the city to the village at a speed of 16 km/h. We need to find out how long each of them traveled before they met, given that the distance between the city and the village is 216 km.

Solution

Let's assume that the motorcyclist traveled for 'x' hours before they met. Since the motorcyclist's speed is 80 km/h, the distance traveled by the motorcyclist is 80x km.

Similarly, the cyclist traveled for 1.5 hours + 'y' hours before they met. Since the cyclist's speed is 16 km/h, the distance traveled by the cyclist is 16(1.5 + y) km.

We know that the total distance between the city and the village is 216 km. Therefore, the sum of the distances traveled by the motorcyclist and the cyclist should be equal to 216 km.

Mathematically, we can represent this as an equation:

80x + 16(1.5 + y) = 216

Now, let's solve this equation to find the values of 'x' and 'y'.

Solving the Equation

To solve the equation, we will simplify and solve for 'y'.

80x + 16(1.5 + y) = 216

80x + 24 + 16y = 216

80x + 16y = 216 - 24

80x + 16y = 192

Divide both sides of the equation by 16:

5x + y = 12

Now, we have a system of equations:

5x + y = 12 (Equation 1) 80x + 16y = 216 (Equation 2)

We can solve this system of equations using the substitution method or the elimination method. Let's use the substitution method.

From Equation 1, we can express 'y' in terms of 'x':

y = 12 - 5x

Substitute this value of 'y' into Equation 2:

80x + 16(12 - 5x) = 216

80x + 192 - 80x = 216

192 = 216

Since the equation is not true, there is no solution that satisfies both equations. This means that the motorcyclist and the cyclist never meet.

Conclusion

Based on the given information, the motorcyclist and the cyclist never meet.