SOLUTION: John can clean a large tank at an aquarium in about 5 hours. When John and Laura work together, they can clean the tank in about 3 hours. About how long would it take Laura to c

Algebra ->  Rate-of-work-word-problems -> SOLUTION: John can clean a large tank at an aquarium in about 5 hours. When John and Laura work together, they can clean the tank in about 3 hours. About how long would it take Laura to c      Log On


   

Question 977590: John can clean a large tank at an aquarium in about 5 hours. When John and Laura work together, they can clean the tank in about 3 hours.
About how long would it take Laura to clean the tank if she works by herself?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
John's rate of cleaning:
[ 1 tank ] / [ 5 hrs ]
I will call Laura's rate of cleaning:
[ 1 tank ] / [ t hrs ]
Their rate of cleaning working together:
[ 1 tank ] / [ 3 hrs ]
---------------------
Add their rates of cleaning to get their
rate working together:
+1%2F5+%2B+1%2Ft+=+1%2F3+
Multiply both sides by +15t+
+3t+%2B+15+=+5t+
+2t+=+15+
+t+=+7.5+
Working by herself, Laura takes 7 hrs and 30 min
to clean the tank
-------------------
check:
+1%2F5+%2B+1%2Ft+=+1%2F3+
+1%2F5+%2B+1%2F7.5+=+1%2F3+
+1%2F5+%2B+2%2F15+=+1%2F3+
+3%2F15+%2B+2%2F15+=+5%2F15+
+5%2F15+=+5%2F15+
OK