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Dennis_Churaev [7]
2 years ago
7

Kate and Jean paint a house together in 6 days. If they work alone, Kate takes 5 fewer days than Jean would take to do the same

job. Which equation represents the time it takes Kate to paint the house by herself?
A. x^2-7x-30=0
B. x^2-5x-30=0
C. 2x-1=0
D. x^2-5x over 6 = 0
Mathematics
1 answer:
frutty [35]2 years ago
3 0
Number of jobs=1

Time: 
<span>Since ‘x’ is given as a variable in the choices, we should reserve it for Kate and use ‘y’ for Jean as follows: </span>
<span>
Kate: => x </span>
<span>Jean: => y </span>

<span>But y = x - 5 </span>

<span>Combined rate: </span>
<span>1/x+ 1/y </span>
<span>= (x + y)/(xy) </span>

<span>Number of jobs done: </span>
<span>
Number of days X combined rate = number of jobs </span>
<span>6 [(x + y)/(xy)] = 1 </span>
<span>6x + 6y = xy </span>
<span>6x + 6(x - 5) = x(x - 5) </span>
<span>6x + 6x - 30 = x² - 5x </span>
<span>12x - 30 = x² - 5x </span>
<span>x² - 17x + 30 = 0 
</span>
Therefore, the answer would be A.
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