Question

Помогите решить!!! Автобус-экспресс отправился отавтовокзала в аэропорт,находящийсяот автовокзала на расстоянии 40 км.Через 10 минут вслед заавтобусом выехал пассажир на. такси.Скорость такси на 20 км\ч больше скорости автобуса.Найдите скорости такси и автобуса.

Answer 1

Аааа, все решил:
60км/ч автобус
80км/ч такси

Я не знаю как в решение записать, но я как то решил: D

Логически всегда почему то, прет.

если бы автобус ехал 40км/ч, то он должен был ехать 1час, -10 минут из-за такси, это 50 минут. чтобы такси ехать 50 минут нужно ехать 50км/ч, но в описание сказано что на 20 минут быстрее, так что :
если автобус едет 60км/ч то ему нужно потратить на путь 40минут -10 минут ,
30 минут нужно потратить такси, т. е. это 80км/ч нужно ехать.

Answer 2

Problem Analysis

We are given that an express bus departs from a bus station to an airport, which is located 40 km away from the bus station. After 10 minutes, a passenger leaves the bus station in a taxi. The speed of the taxi is 20 km/h faster than the speed of the bus. We need to find the speeds of both the taxi and the bus.

Solution

Let's assume the speed of the bus is x km/h. Since the taxi is traveling 20 km/h faster than the bus, its speed will be x + 20 km/h.

To solve this problem, we can use the formula: speed = distance / time.

We know that the distance between the bus station and the airport is 40 km. Let's calculate the time it takes for the bus to reach the airport.

The time taken by the bus can be calculated as follows: time = distance / speed = 40 km / x km/h.

Since the passenger leaves the bus station 10 minutes (or 10/60 hours) after the bus, the time taken by the taxi will be 10/60 hours less than the time taken by the bus.

The time taken by the taxi can be calculated as follows: time = (40 km / x km/h) - (10/60) hours.

Now, let's equate the time taken by the bus and the taxi and solve for x.

(40 km / x km/h) - (10/60) hours = 40 km / (x + 20) km/h

To simplify the equation, we can multiply both sides by x(x + 20) to eliminate the denominators.

40(x + 20) - (10/60)x(x + 20) = 40x

Now, let's solve this equation to find the value of x.

Calculation

Let's solve the equation to find the value of x.

40(x + 20) - (10/60)x(x + 20) = 40x

Simplifying the equation:

40x + 800 - (1/6)x^2 - (1/6)x = 40x

Combining like terms:

800 - (1/6)x^2 - (1/6)x = 0

Multiplying both sides by 6 to eliminate the fraction:

4800 - x^2 - x = 0

Rearranging the equation:

x^2 + x - 4800 = 0

Now, we can solve this quadratic equation to find the value of x.

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 1, and c = -4800.

Calculating the discriminant: b^2 - 4ac = 1^2 - 4(1)(-4800) = 1 + 19200 = 19201.

Taking the square root of the discriminant: √19201 ≈ 138.6.

Using the quadratic formula:

x = (-1 ± 138.6) / (2 * 1)

x = (-1 + 138.6) / 2 ≈ 68.8

x = (-1 - 138.6) / 2 ≈ -69.8

Since the speed cannot be negative, we discard the negative value.

Therefore, the speed of the bus is approximately 68.8 km/h.

The speed of the taxi is 20 km/h faster than the speed of the bus, so the speed of the taxi is approximately 68.8 + 20 = 88.8 km/h.

Answer

The speed of the bus is approximately 68.8 km/h, and the speed of the taxi is approximately 88.8 km/h.