SOLUTION: Benny can clean attic in 8 hours. If Donna helps, it takes them 5 hours. Without help, how long would it take Donna to do the same thing

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Benny can clean attic in 8 hours. If Donna helps, it takes them 5 hours. Without help, how long would it take Donna to do the same thing      Log On


   

Question 988327: Benny can clean attic in 8 hours. If Donna helps, it takes them 5 hours. Without help, how long would it take Donna to do the same thing
Found 2 solutions by josmiceli, macston:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Add their rates of cleaning to get rate working together
Benny's rate:
[ 1 attic cleaned ] / [ 8 hrs ]
-------------------------
Donna's rate:
[ 1 attic cleaned ] / [ t hrs ]
-------------------------
Rate working together:
+1%2F8+%2B+1%2Ft+=+1%2F5+
Multiply both sides by +40t+
+5t+%2B+40+=+8t+
+3t+=+40+
+t+=+13.333+ hrs
Note that +%281%2F3%29%2A60+=+20+ min
Working alone, Donna would take
13 hrs and 20 min to clean the attic
---------------------------------
check answer:
+1%2F8+%2B+1%2Ft+=+1%2F5+
+1%2F8+%2B+1%2F13.333+=+1%2F5+
+.125+%2B+.075+=+.2+
+.2+=+.2+
OK

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Benny: 1 attic/8hours=1/8 attic per hour
working together, in 5 hours Benny cleans (5hr)((1/8)/hr)=5/8 of the attic.
So in 5 hours Donna cleans 3/8 of the attic
Donna: (3/8 attic)/(5hrs)=(3/40) attic/hr
For Donna to clean 1 attic:
(1 attic)/((3/40)attic/hr)=40/3 hours=13.33 hours
.
ANSWER: It would take Donna 13 hours and 20 minutes to clean the attic alone.