SOLUTION: roma can finish weeding a flower garden in 4 1/2 hours. roma has worked for 2 hours before amor joined her and they finished the job in 2 hours. how long would it take both of them

Algebra ->  Rate-of-work-word-problems -> SOLUTION: roma can finish weeding a flower garden in 4 1/2 hours. roma has worked for 2 hours before amor joined her and they finished the job in 2 hours. how long would it take both of them      Log On


   

Question 150565This question is from textbook
: roma can finish weeding a flower garden in 4 1/2 hours. roma has worked for 2 hours before amor joined her and they finished the job in 2 hours. how long would it take both of them to finish the job working together? how long would it take amor to do the job alone? This question is from textbook

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let r= Roma's rate of working
Let a= Amor's rate of working
r+%2B+a+=+t, their rate working together
Roma's rate is (1 garden weeded)/4.5 hrs
1%2F4.5+%2B+a+=+t
What part of the job did Roma do in 2 hours?
%281%2F4.5%29%2A2+=+4%2F9
So, 5%2F9 of the job is left when Amor joins her
They did 5%2F9 of the job in 2 hrs
%285%2F9%29%2F2 is their rate working together
Multiply top and bottom by 9%2F5
%28%289%2F5%29%2F%289%2F5%29%29%2A%28%285%2F9%29%2F2%29+=+1%2F%2818%2F5%29
They can do the whole job in 18%2F5 of an hour
%2818%2F5%29%2A60 = 3 hrs 36 min answer
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To find Amor's time to do the whole job,
1%2F4.5+%2B+a+=+t
2%2F9+%2B+a+=+5%2F18
Multiply both sides by 18
4+%2B+18a+=+5
18a+=+1
a+=+1%2F18 This is Amor's rate, which is
(1 job)/(18 hours)
It takes Amor 18 hrs to do the job alone