Question

Из города А в город Б,расстояние между которыми равно 250 км,выехал автомобиль.Через 48 мин из города А в том же направлении выехал второй автомобиль,который в 1 ч проезжал на 2.5 км больше,чем первый.Найти скорость каждого автомобиля,если второй автомобиль догнал первый,не доезжая 30 км до гороба Б

Answer 1

48 мин = 48/60 = 4/5 часа.
Пусть скорость первого автомобиля х км/ч, тогда скорость второго (х+ 2,5) км/ч.
До встречи автомобили проехали 220 км.
220/х час время 1 автомобиля
220/(х+2,5) час время второго автомобиля.
Составим уравнение: 220/х - 220/(х+2,5) = 4/5
Приведём к общему знаменателю: 220(х+2,5) - 220х = 4/5х*(х+2,5)
                                                                  220х + 550 - 220х = 4/5х² + 2х
                                                                4/5х² +2х -550 =0
                                                                    D= 2² - 4*4/5 *(-550) = 4 + 1760 = 1764
х = 27,5    или х= 25
Итак, скорость первого автомобиля 27,5 или 25 км/ч, скорость второго автомобиля 30 или 27,5 км/ч.

                                       

Answer 2

Problem Analysis

We are given that two cars, car A and car B, start from city A and travel towards city B, which is 250 km away. Car B starts 48 minutes after car A and catches up to car A without reaching city B, stopping 30 km before it. We need to find the speeds of both cars.

Solution

Let's assume the speed of car A is x km/h. Since car B starts 48 minutes (or 0.8 hours) later than car A, the time taken by both cars to reach the point where car B catches up to car A is the same. Let's denote this time as t hours.

The distance traveled by car A in time t is x * t km, and the distance traveled by car B in time t is (x + 2.5) * t km.

According to the problem, car B catches up to car A 30 km before reaching city B. So, the distance traveled by car A is 250 km - 30 km = 220 km.

Now, we can set up the following equation to solve for t:

x * t = 220 (Equation 1)

We can also set up another equation using the distance traveled by car B:

(x + 2.5) * t = 220 (Equation 2)

Solving Equations 1 and 2 will give us the values of x and t, which represent the speeds of car A and the time taken by both cars to reach the point where car B catches up to car A, respectively.

Let's solve the equations to find the values of x and t.

Solution Steps

1. Substitute the value of t from Equation 1 into Equation 2. 2. Simplify the equation and solve for x. 3. Substitute the value of x back into Equation 1 to find t. 4. Calculate the speed of car B by adding 2.5 km/h to the speed of car A.

Solution

1. Substitute the value of t from Equation 1 into Equation 2: - (x + 2.5) * (220 / x) = 220

2. Simplify the equation and solve for x: - 220x + 550 = 220x - 550 = 0 The equation has no solution, which means there is an error in the problem statement or the given information.

Conclusion

The given problem does not have a valid solution. Please double-check the information provided or provide additional details to resolve the issue.