SOLUTION: Krystal can wax a floor in 16 minutes. One day her friend Perry helped her and it only tool 5.76 minutes. How long would it take Perry to do it alone?

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Krystal can wax a floor in 16 minutes. One day her friend Perry helped her and it only tool 5.76 minutes. How long would it take Perry to do it alone?      Log On


   

Question 198755: Krystal can wax a floor in 16 minutes. One day her friend Perry helped her and it only tool 5.76 minutes. How long would it take Perry to do it alone?
Found 2 solutions by user_dude2008, josmiceli:
Answer by user_dude2008(1862) About Me  (Show Source):
You can put this solution on YOUR website!
5.76(1/16+1/x)=1


0.36+5.76/x=1


5.76/x=1-0.36

5.76/x=0.64

5.76=0.64x

5.76/0.64=x

Answer: x=9

Perry can do it in 9 min alone

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This is a problem of adding 2 rates to get a combined rate
In words,
Krystal's rate of working is (1 floor waxed)/(Krystal's time for 1 floor)
Perry's rate of working is (1 floor waxed)/(Perry's time for 1 floor)
and
If I add these rates to get a rate working together,
Krystal and Perry's rate of working is (1 floor waxed)/(K & P time for 1 floor)
and
The problem says that working together, (1 floor waxed)/(5.76 min)
Krystal's rate of working is (1 floor waxed)/ (16 min)
Let t= Perry's time to wax 1 floor working alone
1%2F16+%2B+1%2Ft+=+1%2F5.76
Multiply both sides by 1%2F100
1%2F1600+%2B+1%2F%28100t%29+=+1%2F576
Multiply both sides by 1600%2A576
576+%2B+%2816%2A576%29%2Ft+=+1600
Multiply both sides by t
576t+%2B+9216+=+1600t
1024t+=+9216
t+=+9
Perry, working alone, can wax the floor in 9 minutes
check answer:
1%2F16+%2B+1%2Ft+=+1%2F5.76
1%2F16+%2B+1%2F9+=+1%2F5.76
9%2F%2816%2A9%29+%2B+16%2F%2816%2A9%29+=+100%2F576
9%2F144+%2B+16%2F144+=+25%2F144
25%2F144+=+25%2F144
OK