SOLUTION: Justin and Mark share a bedroom. It takes Justin 4 hours to clean the room alone. It takes Mark 3 hours to clean the room alone. When Justin and Mark worked together on the room, t

Algebra ->  Probability-and-statistics -> SOLUTION: Justin and Mark share a bedroom. It takes Justin 4 hours to clean the room alone. It takes Mark 3 hours to clean the room alone. When Justin and Mark worked together on the room, t      Log On


   

Question 404165: Justin and Mark share a bedroom. It takes Justin 4 hours to clean the room alone. It takes Mark 3 hours to clean the room alone. When Justin and Mark worked together on the room, they both worked for 45 minutes and then Justin fell asleep. Mark (fearing the wrath of his mother) finished the rest of the job while Justin slept. How long did it take them to finish cleaning the room?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Justin's rate: 1%2F4 (1 room in 4 hrs)
Mark's rate: 1%2F3 (1 room in 3 hrs)
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Their rate working together:
+1%2F4+%2B+1%2F3+=+x%2F%283%2F4%29 (x is the fraction of the room they cleaned in 3/4 hr)
1%2F4+%2B+1%2F3+=+%284x%29%2F3
Multiply other sides by 12
3+%2B+4+=+16x
16x+=+7
x+=+7%2F16 (fraction of room cleaned)
So, there is 1+-+7%2F16+=+9%2F16 of the room left to clean
Mark's rate is 1%2F3, so
1%2F3+=+%289%2F16%29%2Ft (t is his time to clean 9%2F16 of a room)
Multiply both sides by 3t
t+=+27%2F16 hr
Note that 3%2F4+=+12%2F16
It took them 12%2F16+%2B+27%2F16+=+39%2F16 hrs
That's 2 hrs + %287%2F16%29%2A60 = 26.25
About 2 hrs and 26 min, unless I made a mistake