Question

Дам 25 баллов!! Студенты отправились на экскурсию на автобусе со скоростью 70 км/ч. Когда они преодолели уже 65 км, а это пятая часть всего пути. Вслед за ними выехал проспавший Пётр с отцом. С какой скоростью должна двигаться машина отца, чтобы догнать автобус не более чем на треть пути?​

Answer 1

Ответ:

Пошаговое объяснение:

весь путь 325 км, получили это тем что 65 км, это 1/5 от пути, то есть 65*5=325

1/3=108

108-65=43км, автобус проедет за 36 мин, 51 сек

отцу нужно проехать расстояние в 108 км за 36 мин 51 сек

то есть скорость 175 км в ч

Answer 2

Problem Analysis

We are given that a group of students is on a bus traveling at a speed of 70 km/h. When they have already traveled 65 km, which is one-fifth of the total distance, Peter and his father start driving to catch up to the bus. We need to determine the speed at which Peter's father's car should travel in order to catch up to the bus before it has traveled more than one-third of the total distance.

Solution

Let's assume the total distance of the trip is D km. We are given that when the students have traveled 65 km, which is one-fifth of the total distance, Peter and his father start driving. This means that the students have already covered 1/5 of the total distance, leaving 4/5 of the total distance to be covered.

We need to find the speed at which Peter's father's car should travel to catch up to the bus before it has traveled more than one-third of the total distance. This means that the bus should not have traveled more than 1/3 of the total distance when Peter's father's car catches up to it.

Let's calculate the distances traveled by the bus and Peter's father's car when they meet.

The distance traveled by the bus when they meet is 65 km, which is 1/5 of the total distance. Therefore, the total distance is:

D = 65 km * 5 = 325 km Now, let's calculate the distance Peter's father's car needs to cover to catch up to the bus. The bus has already traveled 65 km, and we want Peter's father's car to catch up to the bus before it has traveled more than one-third of the total distance. Therefore, the maximum distance the bus can travel is:

Max distance traveled by the bus = (1/3) * D = (1/3) * 325 km = 108.33 km

To catch up to the bus, Peter's father's car needs to cover the remaining distance, which is:

Remaining distance = Total distance - Distance traveled by the bus = 325 km - 65 km = 260 km

Now, we can calculate the speed at which Peter's father's car should travel to cover the remaining distance of 260 km without exceeding the maximum distance traveled by the bus.

Speed of Peter's father's car = Remaining distance / Time taken by the bus to cover the remaining distance

To find the time taken by the bus to cover the remaining distance, we can use the formula:

Time = Distance / Speed

Substituting the values, we have:

Time taken by the bus to cover the remaining distance = Remaining distance / Speed of the bus

Since we know the speed of the bus is 70 km/h, we can calculate the time taken by the bus to cover the remaining distance:

Time taken by the bus to cover the remaining distance = 260 km / 70 km/h = 3.714 hours

Now, we can calculate the speed at which Peter's father's car should travel:

Speed of Peter's father's car = Remaining distance / Time taken by the bus to cover the remaining distance = 260 km / 3.714 hours ≈ 70.01 km/h

Therefore, Peter's father's car should travel at a speed of approximately 70.01 km/h to catch up to the bus before it has traveled more than one-third of the total distance.

Answer

Peter's father's car should travel at a speed of approximately 70.01 km/h to catch up to the bus before it has traveled more than one-third of the total distance.