jack and jerry can complete a job together in 4 hours. if jack require 6 hours to do the job alone, how many hours will it take jerry to do the job alone.
A.12
B.10
C.8
D.6
E.4
jack's rate = 1/6
Jerry's rate = 1/x
combined rate = 1/6 + 1/x
= (x+6)/(6x)
given:
1/( (x+6)/(6x) ) = 4
6x/(x+6) = 4
6x = 4x + 24
2x = 24
x = 12
It would take Jerry to work 12 alone to do the job
check:
combined rate = 1/6 + 1/12
= 3/12 = 1/4
time at combined rate = 1/(1/4) = 4
Thanks
To solve this problem, we can use the concept of rates. Let's denote Jack's rate of completing the job as J (job per hour) and Jerry's rate as M (job per hour).
We know that Jack can complete the job alone in 6 hours, so his rate is 1 job per 6 hours, which is 1/6 J/h.
We also know that Jack and Jerry can complete the job together in 4 hours, which means their combined rate is 1/4 J/h.
Using the idea of rates, we can set up an equation:
J + M = 1/4
Since we know that Jack's rate alone is 1/6 and we want to find Jerry's rate alone, we can substitute M with (1/6) in the equation:
(1/6) + M = 1/4
Now, let's solve for M:
Multiply through by 12 to clear the denominators:
2 + 12M = 3
12M = 3 - 2
12M = 1
M = 1/12
So, Jerry's rate of completing the job alone is 1/12 J/h. This means it would take Jerry 12 hours to do the job alone.
Therefore, the correct answer is A. 12 hours.