Question

автомашина должна была пройти 840 км. В середине пути водитель остановился на обед, а через час продолжил путь. Чтобы прибыть вовремя в пункт назначения, пришлось увеличить скорость на 10 км/ч. Сколько времени занял весь путь, включая время на остановку?

Answer 1

автомашина должна была пройти 840 км.
В середине пути водитель остановился на обед, найдем середину пути
840:2=420 км

теперь перейдем к составлению уравнения
1) Если бы водитель весь путь 840 км ехал с постоянной скоростью х км/час и без обеда, то время на всю дорогу 840/х

2) Но наш водитель ехал так:
420 км со скоростью х км/час - время 420/х
1 час обеда
420 км со скоростью х+10 км/час- время 420/(х+10)

Так как прибыл он во время то время из 1 и 2 случая равны.
составим уравнение

$\displaystyle \frac{420}{x}+ \frac{420}{x+10}+1= \frac{840}{x}\\\\ \frac{420(x+10)+420x}{x(x+10)}= \frac{840}{x}-1\\\\ \frac{420x+4200+420x}{x(x+10)}= \frac{840-x}{x}\\\\ \frac{840x+4200}{x(x+10)}= \frac{(840-x)(x+10)}{x(x+10)}\\\\840x+4200=840x-x^2+8400-10x\\\\x^2+10x-4200=0\\\\D=100+16800=16900=130^2\\\\x_{1.2}= \frac{-10\pm 130}{2}\\\\x_1=60; x_2=-70$

Скорость не может быть отрицательной.
Значит постоянная скорость 60 км/час

Время на всю дорогу 840:60=14 час

Answer 2

Calculation of the Total Time for the Trip

To calculate the total time for the trip, we need to consider the time taken to cover the distance of 840 km and the time spent on the lunch break.

Let's break down the calculation step by step:

1. Distance: The car needs to cover a distance of 840 km. 2. Speed: Initially, the car was traveling at a certain speed. After the lunch break, the speed was increased by 10 km/h. 3. Lunch Break: The driver stopped for lunch and resumed the journey after an hour.

To calculate the total time, we need to consider the time taken to cover the distance at the initial speed and the time taken to cover the remaining distance at the increased speed, including the time spent on the lunch break.

Let's calculate the time for each part of the journey:

1. Time taken to cover the distance of 840 km at the initial speed. 2. Time taken to cover the remaining distance at the increased speed. 3. Time spent on the lunch break.

Finally, we can add these three times together to get the total time for the trip.

Calculation Steps

1. Time taken to cover the distance of 840 km at the initial speed: - Let's assume the initial speed of the car is x km/h. - The time taken to cover a distance of 840 km at the initial speed can be calculated using the formula: time = distance / speed. - Therefore, the time taken to cover the distance of 840 km at the initial speed is 840 / x hours.

2. Time taken to cover the remaining distance at the increased speed: - After the lunch break, the speed was increased by 10 km/h. - Therefore, the speed for the remaining distance is (x + 10) km/h. - The remaining distance can be calculated by subtracting the distance covered before the lunch break (840 km) from the total distance (840 km). - Therefore, the remaining distance is 0 km. - The time taken to cover the remaining distance at the increased speed is 0 hours.

3. Time spent on the lunch break: - The driver stopped for lunch and resumed the journey after an hour. - Therefore, the time spent on the lunch break is 1 hour.

Total Time Calculation

To calculate the total time for the trip, we need to add the time taken to cover the distance at the initial speed, the time taken to cover the remaining distance at the increased speed, and the time spent on the lunch break.

Total time = Time taken to cover the distance at the initial speed + Time taken to cover the remaining distance at the increased speed + Time spent on the lunch break

Total time = (840 / x) + 0 + 1 hours

Please provide the initial speed of the car, and I will calculate the total time for the trip.