SOLUTION: It takes Brenda 15 hours to clean an attic. Danielle can clean the same attic in 13 hours. How long would it take them if they worked together.

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Brenda 15 hours to clean an attic. Danielle can clean the same attic in 13 hours. How long would it take them if they worked together.       Log On


   

Question 1041930: It takes Brenda 15 hours to clean an attic. Danielle can clean the same attic in 13 hours. How long would it take them if they worked together.
Found 2 solutions by josmiceli, Edwin McCravy:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Brenda's rate of working:
[ 1 attic cleaned ] / [ 15 hrs ]
Danielle's rate of working:
[ 1 attic cleaned ] / [ 13 hrs ]
-------------------------
Add their rates of working to get
their rate working together
Let +t+ = time in hrs for them to
clean the attic working together
+1%2F15+%2B+1%2F13+=+1%2Ft+
Multiply both sides by +13%2A15t+
+13t+%2B+15t+=+13%2A15+
+13t+%2B+15t+=+195+
+28t+=+195+
+t+=+6.964+ hrs
--------------------
check the answer:
+1%2F15+%2B+1%2F13+=+1%2Ft+
+.0667+%2B+.0769+=+1%2F6.964+
+.1436+=+.1436+
OK

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Their rates are matrix%281%2C2%2C1%2Cattic%29%2Fmatrix%281%2C2%2C15%2Chours%29 and matrix%281%2C2%2C1%2Cattic%29%2Fmatrix%281%2C2%2C13%2Chours%29

Their combined rate is the sum of their rates 1%2F15%2B1%2F13. 

Since TIME=matrix%281%2C3%2CNUMBER%2COF%2CJOBS%29%2Fmatrix%281%2C3%2CTHEIR%2CCOMBINED%2CRATE%29

Then since they are to do 1 job, the number of jobs is 1, and

1%2F%281%2F15%2B1%2F13%29

Multiply top and bottom by LCD = 15∙13=195

1%2A195%2F%28%281%2F15%2B1%2F13%29%2A195%29

195%2F%28195%2F15%2B195%2F13%29

195%2F%2813%2B15%29

195%2F28

matrix%281%2C2%2C6%2627%2F28%2Chours%29

Edwin