SOLUTION: It takes one crew 4 hours to clean an auditorium after an event. If a second crew helps, it only takes 2.5 hours. How long would it take the second crew, working alone, to clean th

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Question 869447: It takes one crew 4 hours to clean an auditorium after an event. If a second crew helps, it only takes 2.5 hours. How long would it take the second crew, working alone, to clean the auditorium?
_____hours?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
Crew 1 takes 4 hours so their rate is (1/4)auditorium per hour
Let x be the rate in auditoriums per hour of Crew 2
( 1/4 + x )( 2 1/2 hours ) = one clean auditorium
( 1/4 + x )( 5/2 ) = 1
multiply each side by 2/5
( 1/4 + x ) = 2/5
add -1/4 to each side
x = 2/5 -1/4
x = 8/20 -5/20
x = 3/20
3/20 represents 3 auditoriums per 20 hours
or 1 auditorium every 6 2/3 hours ( divide 20 by 3 to get this )