Al completed the job in 20 minutes. Al and Pam completed the job together in 12 minutes. How long does it take Pam to complete the job by herself?
Um, excuse me Mitch, but this is a multiple question answer and the following are the choices:
a. 8 minutes
b. 16 minutes
c. 32 minutes
d. 30 minutes
To find out how long it takes Pam to complete the job by herself, we can set up a proportion using the concept of "work done." The idea is that the amount of work done is directly proportional to the time it takes to complete the work.
Let's assume that the job requires a certain amount of work, represented by "W."
If Al completes the job in 20 minutes, that means Al's work rate is W/20.
If Al and Pam work together and complete the job in 12 minutes, their combined work rate is W/12.
To find out Pam's work rate, we need to determine the difference in work between Al and Pam. Since Al's work rate is W/20, and their combined work rate is W/12, the difference in work rate between them is (W/12) - (W/20).
Next, we can set up a ratio between Pam's work rate and Al's work rate:
Pam's work rate / Al's work rate = Difference in work rate
Pam's work rate / (W/20) = (W/12) - (W/20)
To simplify the equation, let's find a common denominator for the fractions:
Pam's work rate / (W/20) = [(20W/12) - (12W/20)] / (20W/20)
Now, let's simplify further:
Pam's work rate / (W/20) = [(20W * 20)/(12 * 20)] / [(12W * 20)/(20 * 12)]
Pam's work rate / (W/20) = (400W/240) / (240W/240)
Pam's work rate / (W/20) = 400W/240W
Now, we can cross-multiply:
Pam's work rate * 240W = (W/20) * 400W
240Pam * W = 400W^2/20
240Pam = 400W/20
240Pam = 20W
Pam = 20W/240
Pam = W/12
Therefore, it will take Pam 12 minutes to complete the job by herself.