Question

Из села в город выехал автомобиль со скоростью 60 километров в час одновременно с ним из села по той же дороге в город выехал мотоциклист через 2 часа мотоциклист Обогнал автомобиль на 40 километров с какой скоростью он ехал решение задачи

Answer 1

60*2= 120 км - проехал за 2 ч автомобиль

120+40=160 км - проехал за это время мотоцикл

160:2=80км/ч- скорость мотоцикла

Answer 2

Problem Analysis

We are given that a car travels from a village to a city at a speed of 60 kilometers per hour. At the same time, a motorcyclist starts from the village and travels on the same road to the city. After 2 hours, the motorcyclist overtakes the car and is 40 kilometers ahead. We need to find the speed of the motorcyclist.

Solution

Let's assume the speed of the motorcyclist is x kilometers per hour.

After 2 hours, the car has traveled a distance of 60 km/h * 2 h = 120 kilometers.

At this point, the motorcyclist overtakes the car and is 40 kilometers ahead. This means that the motorcyclist has traveled a distance of 120 km + 40 km = 160 kilometers.

We can set up the following equation to find the speed of the motorcyclist:

160 kilometers = x kilometers per hour * (2 hours + t)

where t is the additional time taken by the motorcyclist to overtake the car.

Simplifying the equation, we have:

160 kilometers = 2x kilometers per hour + xt kilometers

Now, we can solve for x:

160 kilometers = 2x kilometers per hour + xt kilometers

160 kilometers = x(2 + t) kilometers per hour

Dividing both sides by (2 + t), we get:

x = 160 kilometers / (2 + t) kilometers per hour

Since the motorcyclist overtakes the car, the additional time t must be greater than 0. Therefore, we can assume t > 0.

Now, we need to find the value of t. We know that the motorcyclist overtakes the car after 2 hours, so t = 0 is not a valid solution.

To find the value of t, we can substitute the given information into the equation:

160 kilometers = 60 kilometers per hour * (2 hours + t)

Simplifying the equation, we have:

160 kilometers = 120 kilometers + 60 kilometers per hour * t

Subtracting 120 kilometers from both sides, we get:

40 kilometers = 60 kilometers per hour * t

Dividing both sides by 60 kilometers per hour, we get:

t = 40 kilometers / 60 kilometers per hour

Simplifying the equation, we have:

t = 2/3 hours

Now, we can substitute the value of t into the equation for x:

x = 160 kilometers / (2 + 2/3) kilometers per hour

Simplifying the equation, we have:

x = 160 kilometers / (8/3) kilometers per hour

Dividing both sides by 1/3, we get:

x = 160 kilometers * 3/8 kilometers per hour

Simplifying the equation, we have:

x = 60 kilometers per hour

Therefore, the motorcyclist was traveling at a speed of 60 kilometers per hour.

Answer

The motorcyclist was traveling at a speed of 60 kilometers per hour.