SOLUTION: If one riveter can do a job in 12 days, and a second riveter can do it in 16 days, how long would it take them to do it together?

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Question 135287This question is from textbook Basic Technical Mathematics with Calculus
: If one riveter can do a job in 12 days, and a second riveter can do it in 16 days, how long would it take them to do it together? This question is from textbook Basic Technical Mathematics with Calculus

Found 2 solutions by solver91311, ptaylor:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
If the first guy can do the job in 12 days, then he can do 1%2F12 of the job in 1 day. Likewise, the other guy can do 1%2F16 of the job in 1 day.

Together, they can do 1%2F12%2B1%2F16 of the job in 1 day. Which means that they will take 1%2F%281%2F12%2B1%2F16%29 days to do the whole job. Just add the two fractions and turn the result over (switch numerator and denominator) to do the arithmetic.

Hint: 12 = 2 X 2 X 3 and 16 = 2 X 2 X 2 X 2, so 2 X 2 X 2 X 2 X 3 is your lowest common denominator.


Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=amount of time needed for both working together
One riviter works at the rate of 1/12 job per day
The second riviter works at the rate of 1/16 job per day
Together they work at the rate of 1/12 + 1/16 job per day, or
4/48 + 3/48 = 7/48 of the job per day. So our equation to solve is:
(7/48)x=1 (1 job, that is) multiply each side by 48
7x=48 divide both sides by 7
x=6 6/7 days or 6.8571 days
Hope this helps -----ptaylor