Question

Павлик виконав домашнє завдання з математики,мови і історії за 2,5год. Завдання з математики він виконав у 1 1/3 рази швидше ніж завдання з мови, а завдання з історіі на півгодини швидше ніж завдання з мови. Скільки часу він затратив на виконання кожного завдання?

Answer 1

Математику Павлик делал 40 мин, родной язык-30 мин, историю-60 мин(1 ч).

Answer 2

Task Analysis

To solve this problem, we need to determine the time it took Pavlik to complete each task (mathematics, language, and history) based on the given information. We know that Pavlik completed the mathematics task 1 1/3 times faster than the language task, and the history task took 30 minutes less than the language task.

Solution

Let's assume that the time taken to complete the language task is x hours.

According to the given information: - The mathematics task was completed 1 1/3 times faster than the language task, so it took (1 + 1/3) * x hours. - The history task took 30 minutes less than the language task, so it took (x - 0.5) hours.

To find the time taken for each task, we can solve the following equation:

x + (1 + 1/3) * x + (x - 0.5) = 2.5

Simplifying the equation:

3x + 4/3 * x - 0.5 = 2.5

Multiplying through by 3 to eliminate the fraction:

9x + 4x - 1.5 = 7.5

Combining like terms:

13x - 1.5 = 7.5

Adding 1.5 to both sides:

13x = 9

Dividing both sides by 13:

x = 9/13

Therefore, the time taken to complete the language task is 9/13 hours.

Now, we can calculate the time taken for each task:

- Mathematics task: (1 + 1/3) * (9/13) hours - Language task: 9/13 hours - History task: (9/13 - 0.5) hours

Simplifying the calculations:

- Mathematics task: 12/13 hours - Language task: 9/13 hours - History task: -5/13 hours

Since the time for the history task is negative, it means that Pavlik finished the history task before starting the language task. Therefore, we can consider the time for the history task as 0 hours.

To summarize, Pavlik spent approximately: - 12/13 hours on the mathematics task - 9/13 hours on the language task - 0 hours on the history task.

Please note that the time values are approximate and may be rounded for simplicity.

Let me know if there is anything else I can help you with!