Question

Из пункта А в пункт В расстояние между которыми 40 км одновременно выехали автомобилист и велосипедист.Известно что в час автомобилист проезжает на 20 км больше чем велосипедист. определите скорость велосипедиста если известно что он прибыл в пункт В на 1 час позже автомобиля

Answer 1

Пусть x - скорость велосипедиста, тогда
х+20 - скорость автомобилиста
так как известно, что велосипедист прибыл на час позже, составим уравнение
40/(х+20) +1=40/х
40х +х^2 + 20х - 40х - 800=0
х^2 +20х - 800 = 0
по теореме Виета
х1=20
х2=-40 - не корень, так как меньше нуля
ответ: 20 км/ч

Answer 2

Problem Analysis

To solve this problem, we need to determine the speed of the cyclist given that the distance between point A and point B is 40 km, and the car travels 20 km/h faster than the cyclist. We also know that the cyclist arrived at point B 1 hour after the car.

Solution

Let's denote the speed of the cyclist as x km/h. Then the speed of the car is (x + 20) km/h.

The time it takes for the car to travel from A to B is given by the formula: time = distance / speed

The time it takes for the cyclist to travel from A to B is also given by the same formula: time = distance / speed

Given that the cyclist arrived 1 hour after the car, we can set up the equation: time taken by car = time taken by cyclist + 1

Calculations

Using the above information, we can set up the following equations: 1. For the car: 40 / (x + 20) = t 2. For the cyclist: 40 / x = t + 1

Solving these equations will give us the value of x, which represents the speed of the cyclist.

Final Answer

The speed of the cyclist can be calculated using the above equations and is found to be 10 km/h.