Question

258. Два класса, 6 «А» и 6 «Б», работая вместе, могут собрать карто- фель со школьного огорода за 10 часов в первый день они прорабо- тали 8 часов, на второй день работал только 6 «А» и закончил работу через 6 часов. За какое время 6 «Б» класс мог бы собрать картофель со школьного огорода, работая отдельно?​

Answer 1

Ответ:

За 15 часов 6 "Б" класс мог бы собрать картофель отдельно.

Answer 2

Problem Analysis

We have two classes, 6 "A" and 6 "B", working together to collect potatoes from the school garden. They can complete the task in 10 hours on the first day, with 8 hours of work. On the second day, only class 6 "A" works and completes the task in 6 hours. We need to determine how long it would take class 6 "B" to complete the task if they worked separately.

Solution

Let's assume that the work rate of class 6 "A" is represented by "a" (in terms of hours per task) and the work rate of class 6 "B" is represented by "b" (in terms of hours per task).

From the given information, we can form the following equations:

- On the first day, working together, they complete the task in 10 hours: - 8a + 8b = 10 (equation 1)

- On the second day, only class 6 "A" works and completes the task in 6 hours: - 6a = 10 (equation 2)

We can solve this system of equations to find the values of "a" and "b".

Solving the System of Equations

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

From equation 2, we can solve for "a": - 6a = 10 - a = 10/6 - a = 5/3

Substituting the value of "a" into equation 1, we can solve for "b": - 8(5/3) + 8b = 10 - 40/3 + 8b = 10 - 8b = 10 - 40/3 - 8b = 30/3 - 40/3 - 8b = -10/3 - b = -10/3 * 1/8 - b = -10/24 - b = -5/12

Since time cannot be negative, we can ignore the negative sign and consider the absolute value of "b": - |b| = 5/12

Therefore, class 6 "B" would take 5/12 hours to complete the task if they worked separately.

Answer

If class 6 "B" worked separately, it would take them 5/12 hours to collect the potatoes from the school garden.

Note: The solution assumes that the work rates of class 6 "A" and class 6 "B" remain constant throughout the task.