Question

На решение задачи Митя затратил 4/5ч больше. Сколько времени выполнили эту работу Оля, если на решение задачи она затратила на 5/12ч меньше, а на решение уравнения - на 1/3ч больше, чем Митя.

Answer 1

4/5 - 5/12 = 23/60
23/60 + 1/3 = 43/60

Answer 2

Problem Analysis

To solve this problem, we need to determine the amount of time Olya spent on solving the task. We are given that Mitya spent 4/5 hours more than Olya on solving the task, Olya spent 5/12 hours less on solving the task, and Olya spent 1/3 hours more on solving the equation than Mitya.

Solution

Let's assume that Mitya spent x hours on solving the task.

According to the given information, Olya spent 5/12 hours less on solving the task than Mitya. Therefore, Olya spent (x - 5/12) hours on solving the task.

Olya also spent 1/3 hours more on solving the equation than Mitya. Therefore, Olya spent (x + 1/3) hours on solving the equation.

Since Olya spent a total of (x - 5/12) hours on solving the task and (x + 1/3) hours on solving the equation, the total time spent by Olya is:

(x - 5/12) + (x + 1/3)

To simplify the expression, we need to find a common denominator for 12 and 3, which is 12.

(x - 5/12) + (x + 1/3) = (12x - 5) / 12 + (4x + 4) / 12

Combining the fractions, we get:

(12x - 5 + 4x + 4) / 12 = (16x - 1) / 12

Therefore, Olya spent (16x - 1) / 12 hours on solving the task and the equation.

To find the value of x, we know that Mitya spent 4/5 hours more than Olya on solving the task. Therefore, we can set up the equation:

x = (16x - 1) / 12 + 4/5

To solve this equation, we can multiply both sides by 12 to eliminate the denominator:

12x = 16x - 1 + 48/5

Multiplying 48/5 by 12/12 to get a common denominator:

12x = 16x - 1 + 576/60

Simplifying the expression:

12x = 16x - 1 + 9.6

Subtracting 16x from both sides:

-4x = -10.6

Dividing both sides by -4:

x = 10.6 / 4

Therefore, Mitya spent approximately 2.65 hours on solving the task.

Now, let's substitute the value of x back into the expression for Olya's time:

(16x - 1) / 12 = (16 * 2.65 - 1) / 12

Calculating the numerator:

(16 * 2.65 - 1) = 42.4 - 1 = 41.4

Substituting the numerator back into the expression:

(16x - 1) / 12 = 41.4 / 12

Calculating the division:

41.4 / 12 ≈ 3.45

Therefore, Olya spent approximately 3.45 hours on solving the task and the equation.

Answer

Olya spent approximately 3.45 hours on solving the task, given that Mitya spent 2.65 hours on the same task.