Question

Растояние между селами 36 км, один велосипедист преодолевает на 1 час быстрее другого. Найти скорость каждого велосипедиста, если известно, что скорость одного на 3км/ч больше скорости другого

Answer 1

Х-скорость медленного
х+3-скорость быстрого
36/х-36/(х+3)=1
36/х-36/(х+3)-1=0 умножим на х(х+3)=х²+3х
36(х+3)-36х-х²+3х=0
36х+108-36х-х²+3х=0
108-х²+3х=0
х²-3х-108=0
D = (-3)² - 4·1·(-108) = 9 + 432 = 441
x1 = (3 - √441)/(2*1) = (3 - 21)/2 = -18/2 = -9
x2 = (3 + √441)/(2*1) = (3 + 21)/2 =24/2 =12-скорость медленного
12+3=15 -скорость быстрого

Answer 2

Calculating the Speed of Each Cyclist

To find the speeds of the two cyclists, we can use the given information about the distance and the time difference between them. Let's denote the speed of the slower cyclist as x km/h and the speed of the faster cyclist as (x + 3) km/h.

The formula to calculate speed is: Speed = Distance / Time

Given: - Distance = 36 km - Time difference = 1 hour

Using the formula, we can set up the following equation: 36 / x - 36 / (x + 3) = 1

Solving this equation will give us the speeds of the two cyclists.

Solving the Equation

Using the given equation 36 / x - 36 / (x + 3) = 1, we can solve for the speeds of the two cyclists.

The solution to the equation is as follows: - x = 9 km/h (speed of the slower cyclist) - x + 3 = 12 km/h (speed of the faster cyclist)

Therefore, the speed of the slower cyclist is 9 km/h and the speed of the faster cyclist is 12 km/h.

This solution satisfies the given conditions of the problem, where the speed of one cyclist is 3 km/h greater than the speed of the other cyclist.