A father can do a job as fast as two sons working together. If one sone does the job alone in three hours and the other does it alone in six hours, how many hours does it take the father to do the job alone?
a. 1
b. 2
c. 3
d. 4
e. 4 1/2
please answer and explain
To solve this problem, we can use the concept of work rates. Let's denote the father's work rate as F (measured in jobs per hour), the first son's work rate as S1, and the second son's work rate as S2.
According to the problem, the father can do a job as fast as two sons working together. This means that the work rate of the father is equal to the combined work rate of the two sons. Mathematically, we can write this as:
F = S1 + S2
We are given that one son can do the job alone in three hours. Since work rate is the reciprocal of time (work rate = 1/time), we can say that the first son's work rate is:
S1 = 1/3 jobs per hour
Similarly, the second son can do the job alone in six hours, so his work rate is:
S2 = 1/6 jobs per hour
Substituting these values into the equation for the father's work rate, we have:
F = 1/3 + 1/6
F = 2/6 + 1/6
F = 3/6
F = 1/2 jobs per hour
The father's work rate is 1/2 jobs per hour, which means he can complete 1/2 of the job in one hour. To find out how many hours it takes for him to complete the whole job, we can take the reciprocal of his work rate:
Time = 1 / F
Time = 1 / (1/2)
Time = 2 hours
Therefore, it takes the father 2 hours to complete the job alone, so the correct answer is (b) 2.
1/x = 1/3 + 1/6
x = 2
So, (B)
Extra credit: how long does it take if all three work together?