Question

Решите задачу: Ученик рассчитывал за 1 5/6 ч. приготовить уроки и за 1 3/4 ч. закончить модель корабля. Однако на всю работу он потратил на 2/5 ч. меньше,чем предполагал. Сколько времени потратил ученик на всю работу?

Answer 1

1 5/6+1 3/4-2/5=11/6+7/4-2/5=110/60+105/60-24/60=191/60=3 11/60 ч=3 часа 11 мин

Answer 2

Problem Analysis

The problem states that a student planned to spend 1 5/6 hours on preparing lessons and 1 3/4 hours on finishing a model ship. However, the student ended up spending 2/5 hours less than planned on the entire task. We need to determine how much time the student actually spent on the entire task.

Solution

To find the total time the student spent on the entire task, we need to add the time spent on preparing lessons and the time spent on finishing the model ship, and then subtract the 2/5 hours that the student spent less than planned.

Let's calculate the total time spent step by step:

1. Convert the mixed fractions 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 time spent on preparing lessons and finishing the model ship: - Total time = 11/6 hours + 7/4 hours

3. Find a common denominator for the fractions: - The common denominator for 6 and 4 is 12.

4. Convert the fractions to have a common denominator: - 11/6 hours = (11/6) * (2/2) = 22/12 hours - 7/4 hours = (7/4) * (3/3) = 21/12 hours

5. Add the fractions: - Total time = 22/12 hours + 21/12 hours = 43/12 hours

6. Subtract the 2/5 hours that the student spent less than planned: - Total time = 43/12 hours - 2/5 hours

To simplify the final answer, we can convert the fraction to a mixed number:

7. Simplify the fraction: - Total time = (43/12) / (1/5) = (43/12) * (5/1) = 215/12 hours

8. Convert the improper fraction to a mixed number: - Total time = 17 11/12 hours

Therefore, the student spent a total of 17 hours and 11 minutes on the entire task.

Answer

The student spent a total of 17 hours and 11 minutes on the entire task.

Explanation

The student initially planned to spend 1 5/6 hours on preparing lessons and 1 3/4 hours on finishing the model ship. However, the student ended up spending 2/5 hours less than planned. By adding the time spent on preparing lessons and finishing the model ship, and then subtracting the 2/5 hours, we calculated that the student spent a total of 17 hours and 11 minutes on the entire task.