Question

Два мотоциклиста приезжают одно и то же расстояние длина которого 64 км скорость первого мотоциклиста на 20 километров час меньше скорости второго поэтому он приезжает данные расстояние надо на 12 минут медленнее чем второй Найдите скорость мотоциклиста Возьмите за X километров час скорость первого мотоциклиста

Answer 1

пусть скорость первого х км/ч тогда второго х+20 км/ час. Расстояние равно 64 км. Значит время первого 64/х часов, а второго 64/х+20 часов. Т. к. разница во времени равна 0,2 часа то составим уравнение  (64/х+20)-(64/х) =0,2

Answer 2

Calculation of the Speed of the First Motorcyclist

To find the speed of the first motorcyclist, let's assume that the speed of the second motorcyclist is X kilometers per hour. According to the given information, the first motorcyclist's speed is 20 kilometers per hour less than the speed of the second motorcyclist.

Therefore, the speed of the first motorcyclist can be expressed as (X - 20) kilometers per hour.

Calculation of the Time Difference

The first motorcyclist takes 12 minutes longer to cover the given distance compared to the second motorcyclist. To calculate the time difference, we need to convert 12 minutes to hours.

12 minutes is equal to 12/60 = 0.2 hours.

Calculation of the Time Taken by Each Motorcyclist

The time taken by each motorcyclist can be calculated using the formula:

Time = Distance / Speed

For both motorcyclists, the distance is given as 64 kilometers.

For the first motorcyclist: Time taken = 64 / (X - 20) hours

For the second motorcyclist: Time taken = 64 / X hours

Calculation of the Time Difference Equation

The time difference equation can be set up as follows:

Time taken by the first motorcyclist - Time taken by the second motorcyclist = 0.2 hours

Substituting the time taken formulas into the equation:

64 / (X - 20) - 64 / X = 0.2

Solving the Equation

To solve the equation, we can multiply both sides by X(X - 20) to eliminate the denominators:

64X - 64(X - 20) = 0.2X(X - 20)

Expanding and simplifying the equation:

64X - 64X + 1280 = 0.2X^2 - 4X

Rearranging the equation:

0.2X^2 - 4X - 1280 = 0

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

Quadratic Equation Solution

Using the quadratic formula:

X = (-b ± √(b^2 - 4ac)) / (2a)

For the equation 0.2X^2 - 4X - 1280 = 0, the coefficients are: a = 0.2 b = -4 c = -1280

Substituting the values into the quadratic formula:

X = (-(-4) ± √((-4)^2 - 4 * 0.2 * (-1280))) / (2 * 0.2)

Simplifying the equation:

X = (4 ± √(16 + 1024)) / 0.4

X = (4 ± √1040) / 0.4

Calculating the square root of 1040:

√1040 ≈ 32.249

Substituting the value into the equation:

X = (4 ± 32.249) / 0.4

Simplifying the equation:

X = (4 + 32.249) / 0.4 ≈ 86.122

X = (4 - 32.249) / 0.4 ≈ -70.622

Since the speed of a motorcyclist cannot be negative, we can discard the negative value.

Therefore, the speed of the first motorcyclist is approximately 86.122 kilometers per hour.

Please note that this calculation is based on the given information and assumptions made.