Question

Автомобиль выехал с постоянной скоростью 75 км/ч из города А в город В, расстояние между которыми равно 275 км. Одновременно с ним из города С в город В, расстояние между которыми равно 255 км, с постоянной скоростью выехал мотоциклист. По дороге он сделал остановку на 50 минут. В результате автомобиль и мотоцикл прибыли в город В одновременно. Найдите скорость мотоциклиста. Ответ дайте в км/ч.

Answer 1

Ответ:

скорость мотоцикла 90 км/час

Пошаговое объяснение:

1.   275км. / 75км/час= 3,7 часа двигалось авто

2.   50 мин остановки = 0,83 часа

3.   3,7 часа - 0,83 часа = 2,83 часа двигалось мото

4.   255км / 2,83ч. = 90 км. /ч. сорость мото

Answer 2

Problem Analysis

We are given that a car travels from city A to city B at a constant speed of 75 km/h, a distance of 275 km. At the same time, a motorcyclist travels from city C to city B, a distance of 255 km, at a constant speed. The motorcyclist makes a 50-minute stop along the way. We need to find the speed of the motorcyclist in km/h.

Solution

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

Let's calculate the time it takes for the car to travel from city A to city B: time_car = distance_car / speed_car = 275 km / 75 km/h.

Now, let's calculate the time it takes for the motorcyclist to travel from city C to city B, taking into account the 50-minute stop: time_motorcycle = (distance_motorcycle / speed_motorcycle) + stop_time.

Since the car and the motorcyclist arrive in city B at the same time, we can equate the two time expressions and solve for the speed of the motorcyclist.

Calculation

Let's substitute the given values into the equations and solve for the speed of the motorcyclist:

time_car = 275 km / 75 km/h = 3.67 hours

time_motorcycle = (255 km / speed_motorcycle) + 50 minutes = (255 km / speed_motorcycle) + 50/60 hours

Since the car and the motorcyclist arrive in city B at the same time, we can equate the two time expressions:

3.67 hours = (255 km / speed_motorcycle) + 50/60 hours

Let's solve this equation for the speed of the motorcyclist.

Solution

To solve the equation, we can first convert the 50 minutes to hours:

50 minutes = 50/60 hours = 0.83 hours

Now, let's substitute the values into the equation and solve for the speed of the motorcyclist:

3.67 hours = (255 km / speed_motorcycle) + 0.83 hours

Subtracting 0.83 hours from both sides of the equation:

3.67 hours - 0.83 hours = 255 km / speed_motorcycle

Simplifying:

2.84 hours = 255 km / speed_motorcycle

To solve for the speed of the motorcyclist, we can rearrange the equation:

speed_motorcycle = 255 km / 2.84 hours

Calculating the speed of the motorcyclist:

speed_motorcycle = 255 km / 2.84 hours ≈ 89.79 km/h

Answer

The speed of the motorcyclist is approximately 89.79 km/h.