Question

Мотоциклист ехал из одного города в другой 4 ч. На обратном пути первые 100 км он ехал с той же скоростью, а затем уменьшил ее на 10 км/ч и поэтому на обратный путь затратил на 30 мин больше. Найти расстояние между городами. Объясните подробно, пожалуйста!!!

Answer 1

Обозначим расстояние за Х

тогда скорость Х/4

 

обратный путь: 100 и еще кусок Х-100

Суммарно он проехал обратно за 4+1/2=4,5 часов

превышение на 0,5 часа получилось на втором куске, т.е. на пути обратно он этот кусок проехал на 0,5 часа дольше

 

второй кусок при движении туда он проехал за (Х-100)/(Х/4)=(4Х-400)/Х часов

второй кусок при движении обратно он проехал за (Х-100)/(Х/4-10)=(4Х-400)/(Х-40) часов

 

Тогда (4Х-400)/(Х-40)-(4Х-400)/Х=0,5

$\frac{4x-400}{x-40}-\frac{4x-400}{x}=\frac{1}{2}$

Умножим на 2Х(Х-40)

$8x^2-800x-8x^2+320x+800x-32000=x^2-40x$

$320x-32000=x^2-40x$

$x^2-40x-320x+32000=0$

$x^2-360x+32000=0$

D=129600-128000=1600

$x_{1,2}=\frac{360\pm40}{2} \ \ \ \ \ \ \ x_1=200 \ \ \ \ \ x_2=160$

 

ОТВЕТ 200 или 160 км

 

Answer 2

Problem Analysis

We are given that a motorcyclist traveled from one city to another in 4 hours. On the return trip, the motorcyclist traveled the first 100 km at the same speed as before, but then reduced the speed by 10 km/h. As a result, the return trip took 30 minutes longer. We need to find the distance between the two cities.

Solution

Let's break down the problem step by step:

1. Let's assume the speed of the motorcyclist during the first part of the return trip (after the first 100 km) is x km/h. 2. We know that the motorcyclist traveled the first 100 km at the same speed as before, so the time taken for this part of the trip is 100 / (x + 10) hours. 3. The remaining distance to be covered on the return trip is the total distance minus the distance covered in the first part of the return trip, which is (total distance - 100) km. 4. The time taken to cover the remaining distance at the reduced speed is (total distance - 100) / x hours. 5. We are given that the return trip took 30 minutes longer than the initial trip, which means the return trip took 4 hours + 30 minutes. 6. We can convert 30 minutes to hours by dividing by 60: 30 minutes / 60 = 0.5 hours. 7. The total time taken for the return trip is the sum of the time taken for the first part of the return trip and the time taken for the remaining distance: (100 / (x + 10)) + ((total distance - 100) / x) = 4.5 hours.

Now, we have an equation with one variable (x) that we can solve to find the value of x. Once we have the value of x, we can calculate the total distance between the two cities.

Let's solve the equation:

(100 / (x + 10)) + ((total distance - 100) / x) = 4.5

To simplify the equation, let's multiply both sides by x(x + 10):

100x + (total distance - 100)(x + 10) = 4.5x(x + 10)

Expanding and simplifying the equation:

100x + (total distance - 100)(x + 10) = 4.5x^2 + 45x

100x + (total distance - 100)x + (total distance - 100)(10) = 4.5x^2 +