Question

Помогите с задачей:Отец и сын работая вместе покрасили забор длиной 168м за 12 часов.Если бы Отец красил забор один он выполнил бы эту работу за 21 час.За сколько часов покрасил бы этот забор сын?

Answer 1

1)168:12=14 (м) красили отец и сын вместе за 1 час. 2)168:21=8 (м) в час красил бы отец один забор. 3) 14-8=6 (м) за 1 час красит сын 4) 168:6=28 (ч) Ответ за 28 часов бы покрасил сын забор

Answer 2

1) 168 : 12 = 14 (м) - столько покрасят отец и сын вместе за 1 час;
2) 168 : 21 = 8 (м) - столько покрасит отец за 1 час;
3) 14 - 8 = 6 (м) - столько покрасит сын за 1 час;
4) 168 : 6 = 28 (ч) - столько времени потребуется сыну, чтобы выкрасить забор самостоятельно.
Ответ: за 28 часов.

Answer 3

Problem Analysis

We are given that a father and son painted a fence together in 12 hours, and if the father painted the fence alone, he would have completed the job in 21 hours. We need to determine how long it would take the son to paint the fence alone.

Solution

Let's assume that the father's painting rate is F and the son's painting rate is S. We can use the formula:

Work = Rate × Time

To solve this problem, we need to set up two equations based on the given information.

Equation 1: When the father and son work together, they complete the job in 12 hours. Equation 2: If the father works alone, he completes the job in 21 hours.

Let's solve these equations to find the values of F and S.

Equation 1:

The combined work rate of the father and son is the sum of their individual work rates:

F + S = 1/12 (since they complete the job in 12 hours)

Equation 2:

The father's work rate is given as:

F = 1/21 (since he completes the job in 21 hours)

Now, we can solve these equations to find the value of S (the son's work rate).

Solving the Equations:

Substituting the value of F from Equation 2 into Equation 1, we get:

(1/21) + S = 1/12

To solve for S, we can subtract (1/21) from both sides of the equation:

S = 1/12 - 1/21

Now, let's find a common denominator for the fractions on the right side of the equation:

S = (7/84) - (4/84) = 3/84

Simplifying the fraction, we get:

S = 1/28

This means that the son's work rate is 1/28 of the job per hour.

Calculating the Time Taken by the Son:

To find the time taken by the son to paint the fence alone, we can use the formula:

Time = Work / Rate

Since the length of the fence is given as 168 meters, the work done by the son alone would be 168 meters.

Substituting the values into the formula, we get:

Time = 168 / (1/28) = 168 × 28 = 4704 hours

Therefore, it would take the son approximately 4704 hours to paint the fence alone.

Answer

The son would take approximately 4704 hours to paint the fence alone.

Verification

To verify the answer, we can check if the combined work rate of the father and son matches the given information.

The combined work rate of the father and son is:

F + S = 1/21 + 1/28 = (4/84) + (3/84) = 7/84

Since they complete the job in 12 hours, their combined work rate should be:

1/12 = 7/84

The combined work rate matches the given information, so our answer is correct.