If a worker takes 4 days to paint a house and another worker takes 8 days to paint the same house. How many days will it take them to paint as a team, considering that they maintain their personal work rhythms?
If one worker takes 4 days to paint the house, that means they paint 1/4 of the house per day. Similarly, if the other worker takes 8 days to paint the house, they paint 1/8 of the house per day.
To find out how long it takes them to paint as a team while maintaining their personal work rhythms, we can add up their individual rates of work.
The first worker paints 1/4 of the house per day and the second worker paints 1/8 of the house per day. In total, they paint 1/4 + 1/8 = 3/8 of the house per day.
Since they paint 3/8 of the house per day, it will take them 8/3 days (or 2 and 2/3 days) to paint the house as a team, if they maintain their personal work rhythms.
To determine how many days it will take them to paint the house as a team, you can use the concept of work rates. The work rate is calculated as the reciprocal of the time taken to complete a task.
Let's denote the work rate of the first worker as R1 (1/4 house per day) and the work rate of the second worker as R2 (1/8 house per day).
To find the combined work rate of the two workers working together, you can add their individual work rates. So the combined work rate, R_total, is R1 + R2.
Therefore, R_total = 1/4 + 1/8 = 2/8 + 1/8 = 3/8 house per day.
Next, we can calculate how many days it will take them to finish the house working at this combined rate.
Let's denote the number of days it takes, when working together, as D_total.
So, according to the formula: (R_total) * (D_total) = 1 (the entire house).
Substituting the values, we have:
(3/8) * (D_total) = 1.
To solve for D_total, we can multiply both sides of the equation by 8/3:
D_total = (8/3) / (3/8) = (8/3) * (8/3) = 64/9 ≈ 7.11.
Therefore, it would take them approximately 7.11 days or about 7 days and 3 hours to paint the house as a team, maintaining their personal work rhythms.