Question

Одна учительница математики может проверить контрольные работы за 3 часа, а вторая – за 4 часа. Найдите, за какое время они могут проверить контрольные работы, если будут работать вместе.

Answer 1

1) 1/3 + 1/4 = 4/12 + 3/12 = 7/12 общая производительность
2) 1 : 7/12 = 12/7 ч = 1 5/7 = 1 час 43 минуты вместе

Answer 2

Весь объём работ принимаем за 1 (целое) :

1) 1 : 3 = 1/3 работ - может проверить 1я за 1 ч
2) 1 : 4 = 1/4 всех работ - может проверить 2я за 1 ч
3) 1/3 + 1/4 = 4/12 + 3/12 = 7/12 - всех работ - проверяют обе за 1 ч
4) 1 : 7/12 = 1 * 12/7 = 1 5/7 ч - за столько проверят обе, работая одновременно.

Answer 3

Calculating the Time Taken to Check Papers

To find out how long it would take for both teachers to check the papers together, we can use the concept of "work done per unit time." Let's calculate the time it would take for both teachers to check the papers together.

- Teacher 1 can check papers in 3 hours. - Teacher 2 can check papers in 4 hours.

To calculate the time it would take for both teachers to check the papers together, we can use the formula:

1 / (time taken by Teacher 1) + 1 / (time taken by Teacher 2) = 1 / (time taken together)

Let's calculate the time taken for both teachers to check the papers together using this formula.

Calculation

Using the formula: 1 / 3 + 1 / 4 = 1 / (time taken together)

Solving for the time taken together: 1 / 3 + 1 / 4 = 7 / 12

So, the time taken for both teachers to check the papers together is 7/12 hours.

Therefore, if both teachers work together, they can check the papers in 7/12 hours.

This calculation is based on the concept of combined work, where the rates of work of the two teachers are added together to find the combined rate of work, and then the time taken for the combined work is calculated.