Question

Из города М в город N ,находящийся на расстоянии 120 км от N,выехал автобус.Через 1 ч вслед за ним выехала легковая машина,скорость которой на 20 км/ч больше скорости автобуса.Найдите скорости автобуса и легковой машины,если они прибыли в город N одновременно.

Answer 1

Скорость автобуса =120/t

Автомобиля =120/(t-1)

т.к. скорость автомобиля больше на 20, то получаем

120/t+20=120/(t-1)

 

(120+20t)*(t-1)=120t

6t+t^2-t-6=6t

t^2-t-6=0

D=25

t=(1+5)/2=3, отрицательный корень нас не интересует

 

Скорость автобуса 120/3=40 км/ч

Автомобиля 40+20 = 60 км/ч

 

Answer 2

Problem Analysis

We are given that a bus leaves city M and travels to city N, which is 120 km away from N. After 1 hour, a car leaves city M as well. The car's speed is 20 km/h faster than the speed of the bus. We need to find the speeds of the bus and the car if they arrive in city N at the same time.

Solution

Let's assume the speed of the bus is x km/h. Since the car's speed is 20 km/h faster than the bus, the speed of the car is x + 20 km/h.

To find the time it takes for each vehicle to travel from city M to city N, we can use the formula:

Time = Distance / Speed

For the bus, the time is given by:

Time for bus = 120 km / x km/h

For the car, the time is given by:

Time for car = 120 km / (x + 20) km/h

Since both vehicles arrive in city N at the same time, the time for the bus and the car should be equal. Therefore, we can set up the following equation:

120 km / x km/h = 120 km / (x + 20) km/h

To solve this equation, we can cross-multiply:

120 km * (x + 20) km/h = 120 km * x km/h

Simplifying the equation:

120x + 2400 = 120x

We can see that the variable x cancels out, leaving us with a constant equation:

2400 = 0

This equation is not possible to solve, as it results in a contradiction. Therefore, there is no solution to this problem.

Conclusion

Based on the given information, there is no solution to the problem. The equation derived from the problem leads to a contradiction, indicating that it is not possible for the bus and the car to arrive in city N at the same time.