Alice takes 4 hours to paint a wall. With sam's help, they can paint the wall in 3 hours. Without help, how long would it take Sam to do the same thing?
1/4 + 1/s = 1/3
Now just solve for s.
12 hours
To solve this problem, we can use the concept of "work rates." The work rate is the amount of work done per unit of time. Let's assume that the work rate of Alice is represented by A, and the work rate of Sam is represented by S.
We are given that Alice takes 4 hours to paint the wall. Therefore, her work rate is 1 wall over 4 hours, which is 1/4 (A = 1/4).
We are also given that with Sam's help, they can paint the wall in 3 hours. Therefore, the combined work rate of Alice and Sam is 1 wall over 3 hours, which is 1/3 (A + S = 1/3).
To find the work rate of Sam alone, we need to subtract Alice's work rate from the combined work rate: S = (A + S) - A.
Substituting the values we already know, we can solve for S:
S = 1/3 - 1/4.
To simplify the calculation, we need to find a common denominator:
S = (4/12) - (3/12).
S = 1/12.
So Sam's work rate is 1/12 wall per hour.
Now, to determine how long it would take Sam to paint the wall alone, we need to find the reciprocal of Sam's work rate:
1 / (1/12).
This is equivalent to multiplying by the reciprocal:
1 * (12/1).
The result is 12 hours.
Therefore, it would take Sam 12 hours to paint the wall alone.