Dan and Dave can work together and paint a house in 4 days
Dan works twice as fast as Dave. How long to paint house alone
If Dan takes x hours, then Dave takes 2x hours.
1/x + 1/(2x) = 1/4
It needs 2 answers
Let's assume that Dave's rate of work is represented by "x" houses per day.
Since Dan works twice as fast as Dave, Dan's rate of work would be "2x" houses per day.
Given that Dan and Dave can complete the painting job in 4 days when working together, we can set up the equation:
(1/4) = 1/(2x) + 1/x
To solve this equation, we can multiply each term by the least common denominator (LCD), which is 4x:
4 = 2 + 4
Simplifying,
4 = 6
This equation is not possible, which means there was an error in the calculations or the problem statement. Please ensure the problem is correctly stated so I can assist you further.
To determine how long it would take for Dan to paint the house alone, we need to find the individual rates at which Dan and Dave work and then calculate the time it takes for Dan alone.
Let's denote Dan's rate as "D" (the amount of work he can complete in one day) and Dave's rate as "V" (the amount of work he can complete in one day).
Given that Dan works twice as fast as Dave, we can write the equation D = 2V.
It is also given that Dan and Dave can complete the entire house in 4 days when working together. We can express this as the equation D + V = 1/4, where "1" represents the whole house.
Now, we can solve the system of equations to find the rates of Dan and Dave. Let's solve for V in the first equation and substitute it into the second equation:
D = 2V
V = D/2
Substituting V = D/2 into D + V = 1/4:
D + D/2 = 1/4
2D + D = 1/4
3D = 1/4
D = 1/4 * (1/3)
D = 1/12
So, Dan's rate of work is 1/12 of the house per day. To determine how long Dan would take to complete the whole house alone, we can calculate the reciprocal of D:
1 / D = 1 / (1/12) = 12
Therefore, it would take Dan 12 days to paint the house alone.