Question

Велосипедист проехал 24 км, а мотоциклист – 10 км. Скорость мотоциклиста на 18 км/ч больше скорости велосипедиста. Найдите скорости обоих, если известно, что велосипедист был в пути на 1 час больше, чем мотоциклист.

Answer 1

Ответ:

Пошаговое объяснение:

Пусть х- скорость велосипедиста, (х+18)- скорость мотоциклиста

24/х- времени затратил велосипедист, 10/(х+18)- времени затратит мотоциклист

Отбросим знаменатель:

24x+432-10x=x^2+18x

x^2+18x-24x-432+10x=0

x^2+4x-432=0

x1=16-/2=8-=8-2- не подходит

x2=8+2- скорость велосипедиста

26+-скорость мотоциклиста

Answer 2

Problem Analysis

We are given that a cyclist traveled 24 km and a motorcyclist traveled 10 km. The motorcyclist's speed is 18 km/h faster than the cyclist's speed. We also know that the cyclist was on the road for 1 hour longer than the motorcyclist. We need to find the speeds of both the cyclist and the motorcyclist.

Solution

Let's assume the speed of the cyclist is x km/h. Since the motorcyclist's speed is 18 km/h faster, the speed of the motorcyclist is x + 18 km/h.

We can use the formula distance = speed × time to create two equations based on the given information.

For the cyclist: 24 = x × (t + 1), where t is the time in hours for the motorcyclist.

For the motorcyclist: 10 = (x + 18) × t

We can solve this system of equations to find the values of x and t.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From the first equation, we can express t in terms of x: t = (24 / x) - 1

Substituting this value of t into the second equation, we get: 10 = (x + 18) × ((24 / x) - 1)

Simplifying the equation: 10 = (x + 18) × (24 / x) - (x + 18)

Expanding and rearranging the equation: 10 = (24(x + 18) / x) - (x + 18)

Multiplying through by x to eliminate the denominator: 10x = 24(x + 18) - x(x + 18)

Expanding and simplifying: 10x = 24x + 432 - x^2 - 18x

Rearranging the equation: x^2 + 32x - 432 = 0

Now we can solve this quadratic equation to find the value of x.

Solving the Quadratic Equation

We can solve the quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula.

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the coefficients are: a = 1, b = 32, c = -432

Substituting these values into the quadratic formula, we get: x = (-32 ± √(32^2 - 4(1)(-432))) / (2(1))

Simplifying: x = (-32 ± √(1024 + 1728)) / 2

x = (-32 ± √2752) / 2

x = (-32 ± 52.49) / 2

Now we have two possible values for x: x = (-32 + 52.49) / 2 or x = (-32 - 52.49) / 2

Calculating these values, we get: x = 10.245 or x = -42.245

Since speed cannot be negative, we discard the negative value.

Therefore, the speed of the cyclist is 10.245 km/h.

To find the speed of the motorcyclist, we can substitute this value of x into one of the original equations: 10 = (10.245 + 18) × t

Simplifying: 10 = 28.245 × t

Solving for t: t = 10 / 28.245

Calculating this value, we get: t ≈ 0.354 hours

Therefore, the speed of the motorcyclist is 28.245 km/h and the time taken by the motorcyclist is approximately 0.354 hours.

Answer

The speed of the cyclist is approximately 10.245 km/h and the speed of the motorcyclist is approximately 28.245 km/h. The motorcyclist took approximately 0.354 hours to travel the given distance.