Question

З міста А в місто В виїхав велосипедист. Через 3 год у тому ж напрямі з міста А виїхав мотоцикліст і прибув в місто В одночасно з велосипедистом. Знайдіть швидкість велосипедиста, якщо вона менша за швидкість мотоцикліста на 45 км/год, а відстань між містами дорівнюе 60 км.

Answer 1

Х км/ч - скорость вело
х+45 км/ч - скорость мото
60/х ч - время в пути вело
60/(х+45) ч - время в пути мото, на 3 ч меньше

60/х - 60/(х+45)=3
60(х+45-х)=3х(х+45)
3х²+135х -2700=0
х²+45х -900=0
D=45²+4*900=5625=+-75²
х1= (-45-75)/2= - 60 - не подходит решению
х2=(-45+75)/2=15(км/ч) - скорость вело

Answer 2

Problem Analysis

We are given the following information: - A cyclist traveled from city A to city B. - After 3 hours, a motorcyclist traveled in the same direction from city A to city B and arrived at city B at the same time as the cyclist. - The speed of the cyclist is 45 km/h less than the speed of the motorcyclist. - The distance between city A and city B is 60 km.

We need to find the speed of the cyclist.

Solution

Let's assume the speed of the cyclist is x km/h. Since the speed of the motorcyclist is 45 km/h faster, the speed of the motorcyclist is x + 45 km/h.

We can use the formula distance = speed × time to find the distance traveled by each person.

For the cyclist: - Speed = x km/h - Time = 3 hours - Distance = x × 3 km

For the motorcyclist: - Speed = x + 45 km/h - Time = t hours (to be determined) - Distance = (x + 45) × t km

Since both the cyclist and the motorcyclist arrived at city B at the same time, their distances traveled must be equal. Therefore, we can set up the equation:

x × 3 = (x + 45) × t

We also know that the distance between city A and city B is 60 km, so we can set up another equation:

x × 3 = 60

Now we have a system of two equations with two variables. We can solve this system to find the value of x, which represents the speed of the cyclist.

Solving the System of Equations

Let's solve the system of equations:

x × 3 = (x + 45) × t (Equation 1)

x × 3 = 60 (Equation 2)

From Equation 2, we can solve for x:

x = 60 / 3

Simplifying, we get:

x = 20

Now we can substitute the value of x into Equation 1:

20 × 3 = (20 + 45) × t

Simplifying, we get:

60 = 65t

Solving for t, we get:

t = 60 / 65

Simplifying, we get:

t ≈ 0.9231

Therefore, the speed of the cyclist is approximately 20 km/h.

Answer

The speed of the cyclist is approximately 20 km/h.