Question

Поезд вышел со станции с опозданием на 20 минут, но, повысив на 16 км/ч плановую скорость, через 160 км ликвидировал опоздание.Найдите плановую скорость.

Answer 1

Уравнение:160/х-160/х+16=1/3,x^2+16x-7680=0.Д=7744=88^2. x=-8+88=80

Answer 2

Calculation of Planned Speed

To find the planned speed, we can use the information provided in the question. The train departed from the station 20 minutes late but was able to make up for the delay by increasing its speed by 16 km/h over a distance of 160 km.

Let's assume the planned speed of the train is x km/h.

The train's delay can be calculated by multiplying the time it was late (20 minutes) by the planned speed: 20 minutes = (20/60) hours = 1/3 hours

The distance covered during the delay can be calculated by multiplying the delay time by the planned speed: Distance covered during delay = (1/3) * x km

The remaining distance to be covered after the delay is 160 km.

To eliminate the delay, the train increased its speed by 16 km/h. Therefore, the effective speed after the delay is (x + 16) km/h.

The time taken to cover the remaining distance after the delay can be calculated using the formula: Time = Distance / Speed

The time taken to cover the remaining distance is: Time = 160 km / (x + 16) km/h

Since the train was able to cover the remaining distance without any delay, the time taken to cover the remaining distance is equal to the delay time: Time = 1/3 hours

Now we can set up an equation to solve for the planned speed:

(160 km) / (x + 16 km/h) = 1/3 hours

To solve this equation, we can cross-multiply and solve for x:

160 km = (1/3) hours * (x + 16) km/h

160 km = (x + 16) km/h * (1/3) hours

160 km = (x + 16) km * (1/3) hours

160 km * 3 hours = (x + 16) km * 1

480 km/hours = x + 16 km

480 km/hours - 16 km = x

464 km/h = x

Therefore, the planned speed of the train is 464 km/h.