Question 103822
<font size = 7 color = "red"><b>
MATHLOVER'S SOLUTION IS INCORRECT!
`
CORRECT SOLUTION BY EDWIN:</font>
<font face = "lucida console"><b>
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/K}}} 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/(K-5)}}} 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/(K-5)}}} = {{{600/K}}} + {{{20}}}
`
Solve that by first multiplying thru by LCD of K(K-5)
`
{{{K(K-5)}}}{{{600/(K-5)}}} = {{{K(K-5)}}}{{{600/K}}} + {{{K(K-5)}}}{{{20}}}
`
{{{600K}}} = {{{600(K-5)}}} + {{{20K(K-5)}}}
`
{{{600K}}} = {{{600K}}} - {{{3000}}} + {{{20K^2}}} - {{{100K}}}
`
{{{0}}} = {{{20K^2}}} - {{{100K}}} - {{{3000}}}
`
Divide every term on both sides by 20:
`
{{{0/20}}} = {{{(20K^2)/20}}} - {{{(100K)/20}}} - {{{3000/20}}}
`
{{{0}}} = {{{K^2}}} - {{{5K}}} - 150
`
Factoring:
`
{{{0}}} = {{{(K-15)(K+10)}}}
`
Setting the first factor = 0, {{{K-15=0}}} or {{{K=15}}}
Setting the second factor = 0, {{{K+10=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