Question

Ученица рассчитывала за 1 5/6 ч приготовить уроки и за 1 3/4 ч сшить платье. Однако на всю работу она затратила на 2/5ч меньше, чем она рассчитывала. Сколько времени потратила ученица на всю эту работу?

Answer 1

To solve this problem, we need to find the total time the student spent on both preparing lessons and sewing the dress.

Let's break down the information given:

- The student planned to spend 1 5/6 hours preparing lessons. - The student planned to spend 1 3/4 hours sewing the dress. - However, the student ended up spending 2/5 hours less than planned on the entire task.

To find the total time the student spent on both tasks, we can add the planned time for preparing lessons and sewing the dress, and then subtract the time saved:

1. Convert the mixed numbers to improper fractions: - 1 5/6 hours = (6 * 1 + 5) / 6 = 11/6 hours - 1 3/4 hours = (4 * 1 + 3) / 4 = 7/4 hours

2. Add the planned times for preparing lessons and sewing the dress: - 11/6 hours + 7/4 hours = (11 * 4 + 7 * 6) / (6 * 4) = 44/24 + 42/24 = 86/24 hours

3. Subtract the time saved (2/5 hours) from the total planned time: - 86/24 hours - 2/5 hours = (86 * 5 - 2 * 24) / (24 * 5) = 430/120 - 48/120 = 382/120 hours

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

- 382/120 hours = (382 ÷ 2) / (120 ÷ 2) = 191/60 hours

Therefore, the student spent 191/60 hours on the entire task.

Please note that the time is given in fraction form, and it can also be expressed as a mixed number (3 11/60 hours) or a decimal (3.1833 hours) if needed.