Question

Автобус, проехав с некоторой скоростью часть пути, полчаса простоял из-за аварии. Чтобы на оставшихся 210 км пути наверстать потерянное время, водитель автобуса увеличил скорость на 10 км/ч. В конечный пункт автобус прибыл по расписанию. Найдите, с какой скоростью проехал автобус первую часть пути?

Answer 1

Пусть Х км/ч - начальная скорость автобуса. Если бы автобус не останавливался, то оставшиеся 210 км он бы проехал за время 210/Х часов. Но он простоял 1/2ч и делее поехал со скоростью (Х+10) км/ч и приехал вовремя, т.е. за то же время, если бы двигался со скоростью Х и не останавливался.
Получаем равенство: 210/Х=1/2+210/(Х+10)
Приводим к общему знаменателю и сокращаем, получим Х^2+10X-4200=0
Х1= -70 - не подходит по смыслу
Х2=60
Ответ 60 км/ч

Answer 2

Problem Analysis

We are given that a bus traveled a certain distance at a certain speed, but had to stop for half an hour due to an accident. To make up for the lost time, the driver increased the speed by 10 km/h for the remaining distance. We need to find the speed at which the bus traveled the first part of the journey.

Solution

Let's assume that the initial speed of the bus was x km/h. We are also given that the bus traveled a certain distance before the accident, but we don't know the exact value. Let's call this distance d km.

We can calculate the time it took for the bus to travel the first part of the journey using the formula:

Time = Distance / Speed

So, the time taken for the first part of the journey is:

Time1 = d / x

After the accident, the bus had to make up for the lost time by increasing its speed by 10 km/h. The remaining distance is given as 210 km. We can calculate the time taken for the remaining distance using the same formula:

Time2 = 210 / (x + 10)

The total time taken for the journey is the sum of the time taken for the first part and the time taken for the remaining distance:

Total Time = Time1 + Time2

Since the total time taken for the journey is given as the scheduled time, we can set up the equation:

Total Time = Scheduled Time

Substituting the values, we get:

d / x + 210 / (x + 10) = Scheduled Time

Now, we can solve this equation to find the value of x, which represents the speed at which the bus traveled the first part of the journey.

Let's calculate the value of x using the given information.