SOLUTION: "Find the time for two people working together to complete a task if it takes them 4.5 hours and 6 hours individually." I tried working this problem out, but I had a hard time.

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Question 908281: "Find the time for two people working together to complete a task if it takes them 4.5 hours and 6 hours individually."
I tried working this problem out, but I had a hard time. I checked the solutions manual, but they used a random 27 in the equation somehow. Not I am just super confused! Thanks for your help!
Found 2 solutions by richwmiller, ankor@dixie-net.com:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
27 is not random
4.5*6=27
1/a+1/b=1/x
1/4.5+1/6=1/x
6/27.0+4.5/27.0=1/x
10.5/27.0=1/x
x=27.0/10.5
x=2.57142857 hours working together
check
x/a+x/b=1
x/4.5+x/6=1
2.57142857/4.5+2.57142857/6=1
0.57142857+0.42857143=1
1.0=1
ok

Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
"Find the time for two people working together to complete a task if it takes them 4.5 hours and 6 hours individually."
:
Let t = time to complete the job working together
Let the completed job = 1
:
Each will do a fraction of the job, the two fractions add up to 1
:
+ = 1
multiply by 36, get rid of the denominators
36* + 36* = 1*36
Cancel the denominators and you have
8t + 6t = 36
14t = 36
t= 36/14
t = 2.57 hrs working together; that's, 2 + .57(60) = 2 hr 34.2 min