Question

Саша сможет покрасить забор на даче за 10 часов. Если будет работать Сергей, то четверть работы он выполнит за 3 часа, а Толя половину забора может покрасить за 7,5 часов. За сколько времени они покрасят забор, работая вместе?

Answer 1

Ответ будет таким сложным 21.50.

Answer 2

Problem Analysis

We are given the information that Sasha can paint a fence at the dacha in 10 hours. Sergey can complete a quarter of the work in 3 hours, and Tolya can paint half of the fence in 7.5 hours. We need to determine how long it will take for them to paint the fence together.

Solution

Let's calculate the individual rates of work for each person first: - Sasha can paint the entire fence in 10 hours, so her rate of work is 1/10 of the fence per hour. - Sergey can complete a quarter of the work in 3 hours, so his rate of work is 1/4 of the fence per 3 hours, which is equivalent to 1/12 of the fence per hour. - Tolya can paint half of the fence in 7.5 hours, so his rate of work is 1/2 of the fence per 7.5 hours, which is equivalent to 1/15 of the fence per hour.

To find the combined rate of work when they work together, we can add up their individual rates of work: - Sasha's rate: 1/10 of the fence per hour. - Sergey's rate: 1/12 of the fence per hour. - Tolya's rate: 1/15 of the fence per hour.

Adding these rates together, we get: 1/10 + 1/12 + 1/15 = (18 + 15 + 12)/(180) = 45/180 = 1/4

This means that when they work together, they can paint 1/4 of the fence per hour.

To find the total time it will take for them to paint the entire fence, we can divide the total work (1 fence) by their combined rate of work (1/4 fence per hour): 1 / (1/4) = 4 hours.

Therefore, it will take them 4 hours to paint the fence together.

Answer

Working together, Sasha, Sergey, and Tolya will be able to paint the fence at the dacha in 4 hours.