SOLUTION: Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If connie types at a rate of 20 words per minute faster than Katie types, find the typing rate of

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If connie types at a rate of 20 words per minute faster than Katie types, find the typing rate of      Log On


   

Question 103822: Connie can type 600 words in 5 minutes less than it takes Katie to type 600 words. If connie types at a rate of 20 words per minute faster than Katie types, find the typing rate of each woman.
Found 2 solutions by MathLover1, Edwin McCravy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
We know that amount of words is equal Rate+%2A+Time
If Connie types at a rate of {{[20}}} words per minute faster than Katie types
we have:
600+=+20+%2A+Time
Time+=+600+%2F+20+ = > Time+=+30min
which means that Connie types 600 words in 30 minutes.
Now find it for Katie: since Connie can type 600 words in 5 minutes less than it takes Katie, we will have
Time+=+30+%2B+5 = > Time+=+35min
now, let find the rate for Katie:
600+=+Rate+%2A+35
Rate+=+600+%2F+35+
Rate=+120+%2F+7+
Rate+=+17.14
Katie types 17.14%29 words per minute.

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

MATHLOVER'S SOLUTION IS INCORRECT!
`
CORRECT SOLUTION BY EDWIN:

Connie can type 600 words in 5 minutes less than it takes Katie to type 600
words. If connie types at a rate of 20 words per minute faster than Katie
types, find the typing rate of each woman.
`
Suppose it takes Katie K minutes to type 600 words.
`
Then Katie's rate = (600 words)/(K minutes) = 600%2FK words/minute.
`
Then from this sentence:
`
>>...Connie can type 600 words in 5 minutes less than it takes Katie to type
600 words...<<
`
Connie's time to type 600 words is K-5 minutes.
`
Then Connie's rate = (600 words)/(K-5 minutes) = 600%2F%28K-5%29 words/minute.
`
Then from this sentences:
`
>>...connie types at a rate of 20 words per minute faster than Katie
types...<<
`
we form our equation:
`
Connie's rate = Katie's rate + 20 words/minute.
`
600%2F%28K-5%29 = 600%2FK + 20
`
Solve that by first multiplying thru by LCD of K(K-5)
`
K%28K-5%29600%2F%28K-5%29 = K%28K-5%29600%2FK + K%28K-5%2920
`
600K = 600%28K-5%29 + 20K%28K-5%29
`
600K = 600K - 3000 + 20K%5E2 - 100K
`
0 = 20K%5E2 - 100K - 3000
`
Divide every term on both sides by 20:
`
0%2F20 = %2820K%5E2%29%2F20 - %28100K%29%2F20 - 3000%2F20
`
0 = K%5E2 - 5K - 150
`
Factoring:
`
0 = %28K-15%29%28K%2B10%29
`
Setting the first factor = 0, K-15=0 or K=15
Setting the second factor = 0, K%2B10=0 or K=-10
`
Discarding the negative answer, Katie's time for typing 600
word is 15 minutes, so
`
Katie's rate is (600 words)/(15 minutes) = 600/15 words/minute
or 40 words/minute
`
Connie's time for typing 600 words is 5 minutes less than
Katie's time for typing 600 words, so her time is 15-5 or 10
minutes, so
`
Connie's rate is (600 words)/(10 minutes) = 600/10 words/minute
of 60 words/minute.
`
This checks with
`
>>...connie types at a rate of 20 words per minute faster than Katie
types...<<
`
Edwin