Question

Первый процессор обработал данные на 15 секунд быстрее второго. Оба процессора, работая одновременно, обработали данные за 18 секунд. Определите за сколько секунд каждый из процессоров обработает данные по отдельности.

Answer 1

t1=t2-15

tобщее=t1t2/(t1+t2)=(t2-15)t2/(2t2-15)=(t2^2-15t2)/2t2-15)=18

t2^2-15t2=36t2-15*18
t2^2-51t2+15*18=0

D=39^2

t2=(51+-39)/2=45,6

t1=30 или -9

время отрицательно в современной физике быть не может значит ответ 30

Answer 2

Problem Analysis

We are given that the first processor processed the data 15 seconds faster than the second processor. When both processors worked simultaneously, they processed the data in 18 seconds. We need to determine how long each processor would take to process the data individually.

Solution

Let's assume that the second processor takes x seconds to process the data. Since the first processor processed the data 15 seconds faster than the second processor, it would take (x - 15) seconds for the first processor to process the data.

When both processors work simultaneously, they process the data in 18 seconds. This means that the combined processing rate of both processors is 1/18 of the data per second.

To find the individual processing rates of each processor, we can set up the following equation:

1/(x - 15) + 1/x = 1/18

Simplifying this equation will allow us to solve for x, which represents the time taken by the second processor.

Calculation

Let's solve the equation to find the value of x:

1/(x - 15) + 1/x = 1/18

Multiplying through by 18x(x - 15) to eliminate the denominators:

18x + 18(x - 15) = x(x - 15)

Expanding and simplifying:

18x + 18x - 270 = x^2 - 15x

36x - 270 = x^2 - 15x

Rearranging the equation:

x^2 - 51x + 270 = 0

Using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -51, and c = 270.

Calculating the values of x using the quadratic formula:

x = (-(-51) ± sqrt((-51)^2 - 4(1)(270))) / (2(1))

x = (51 ± sqrt(2601 - 1080)) / 2

x = (51 ± sqrt(1521)) / 2

x = (51 ± 39) / 2

So, we have two possible values for x: x = 45 and x = 6.

If x = 45, then the first processor would take (45 - 15) = 30 seconds to process the data.

If x = 6, then the first processor would take (6 - 15) = -9 seconds to process the data. However, since time cannot be negative, this value is not valid.

Therefore, the second processor takes 45 seconds to process the data, and the first processor takes (45 - 15) = 30 seconds to process the data.

Answer

The second processor takes 45 seconds to process the data, while the first processor takes 30 seconds to process the data.