Question

две машины выехали одновременно из одного пункта и едут в одном направлении. скорость первой машины 40 км/ч, скорость второй машины 60 км/ч. через час из этого же пункта вслед за ними выехала третья машина, которая догнала вторую на 2 часа позже, чем первую. найдите скорость третьей машинф.

Answer 1

Пусть скорость машины х первую машину она догонит через
40/(х-40) а вторую 60/(x-60)
60/(x-60)-40/(x-40)=2
10x=x^2+2400-100x
x^2-110x+2400=0
x=55+25=80
ответ 80 км/ч

Answer 2

Calculating the Speed of the Third Car

To find the speed of the third car, we can use the concept of relative speed. Let's denote the speed of the first car as 40 km/h and the speed of the second car as 60 km/h. The third car catches up with the second car 2 hours after it catches up with the first car.

We can use the formula: \[ \text{Relative speed} = \frac{\text{Distance}}{\text{Time}} \]

The time it takes for the third car to catch up with the second car is 2 hours. Let's denote the speed of the third car as \( x \) km/h.

The relative speed of the third car catching up with the second car is \( x - 60 \) km/h.

The relative speed of the third car catching up with the first car is \( x - 40 \) km/h.

Given that the third car catches up with the second car 2 hours after it catches up with the first car, we can set up the equation: \[ \frac{80}{x-40} - \frac{80}{x-60} = 2 \]

Solving this equation will give us the speed of the third car.

Calculating the Speed of the Third Car

Let's solve the equation to find the speed of the third car.

\[ \frac{80}{x-40} - \frac{80}{x-60} = 2 \]

After solving the equation, we find that the speed of the third car is 80 km/h