SOLUTION: Batman can clean up all of the crime in Gotham city in 8hr working alone. Robin can do the same job alone in 12hr. If Robin starts crime fighting at 8 A.M. and Batman joins him a

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Batman can clean up all of the crime in Gotham city in 8hr working alone. Robin can do the same job alone in 12hr. If Robin starts crime fighting at 8 A.M. and Batman joins him a      Log On


   

Question 122330: Batman can clean up all of the crime in Gotham city in 8hr working alone. Robin can do the same job alone in 12hr. If Robin starts crime fighting at 8 A.M. and Batman joins him at 10 A.M.. then at what time will they have all of the crime cleaned up?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Batman can clean up all of the crime in Gotham city in 8hr working alone. Robin can do the same job alone in 12hr. If Robin starts crime fighting at 8 A.M. and Batman joins him at 10 A.M.. then at what time will they have all of the crime cleaned up?
:
Let t = time spent by Batman to wipe out crime
then
(t+2) = time spent by Robin to wipe out crime
:
Let the completed job = 1
:
t%2F8%29 + %28%28t%2B2%29%29%2F12 = 1
:
Multiply equation by 24 to get rid of the denominators
24*t%2F8%29 + 24*%28%28t%2B2%29%29%2F12 = 24(1)
Cancel out the denominators and you have:
:
3t + 2(t+2) = 24
:
3t + 2t + 4 = 24
:
5t = 24 - 4
t = 20%2F5
t = 4 hrs Batman's time which started at 10 AM, therefore
Completed job will be at 2 PM
:
:
Check solution:
4%2F8%29 + 6%2F12 = 1; confirms our solution