Question

автомобиль должен проехать 840 км за определенное время. На половине пути он был задержался на 30 мин из за технической неисправности. Чтобы прибыть вовремя, ему пришлось увеличить скорость на 2км/ч. Сколько времени автомобиль находился в пути?

Answer 1

х-км/ч скорость мотоциклиста
840/х - планируемое время мотоциклиста от А до Б
420/х-время за которое мотоциклист проехал первую половину пути
420/(х+2) -время за которое мотоциклист проехал вторую половину пути
420/х+420/(х+2)+1/2=840/х
420/(х+2)+1/2=420/х
420/х-420/(х+2)=1/2
(420х+840-420х)/(х(х+2))=1/2
x^2+2x=1680
x^2+2x-1680=0, D=2^2-4*1680=4+6720=6724, x1=(-2+82)/2=40, x2=(-2-82)/2=-42(посторонний корень)
840/40=21. Ответ Проехал за 21 час

Answer 2

Calculation of the Total Travel Time

To calculate the total travel time of the car, we need to consider the following information:

- The car needs to travel a distance of 840 km. - It was delayed for 30 minutes at the halfway point due to a technical issue. - To arrive on time, the car had to increase its speed by 2 km/h.

To calculate the total travel time, we can follow these steps:

1. Calculate the time taken to travel the first half of the distance at the original speed. 2. Subtract the delay time of 30 minutes. 3. Calculate the time taken to travel the second half of the distance at the increased speed. 4. Add the times calculated in steps 1, 2, and 3 to get the total travel time.

Let's calculate the total travel time step by step.

1. Time taken to travel the first half of the distance at the original speed: - The total distance is 840 km, so the distance for the first half is 840 km / 2 = 420 km. - The original speed is not mentioned in the question, so we'll assume it to be x km/h. - Time taken to travel the first half = distance / speed = 420 km / x km/h = 420/x hours.

2. Subtract the delay time of 30 minutes: - 30 minutes is equal to 30/60 = 0.5 hours. - Adjusted time taken to travel the first half = 420/x - 0.5 hours.

3. Time taken to travel the second half of the distance at the increased speed: - The distance for the second half is also 420 km. - The increased speed is the original speed + 2 km/h = x + 2 km/h. - Time taken to travel the second half = distance / speed = 420 km / (x + 2) km/h = 420/(x + 2) hours.

4. Total travel time: - Total travel time = adjusted time taken to travel the first half + time taken to travel the second half. - Total travel time = 420/x - 0.5 + 420/(x + 2) hours.

Now, let's simplify the equation and calculate the total travel time.

Total travel time = 420/x - 0.5 + 420/(x + 2) hours.

Please note that we do not have enough information to calculate the exact value of the total travel time without knowing the original speed of the car.