Question

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-6=0 C. 2x-1=0 D. X^2-5x/6=0

Answer 1

Answer: $x^2-17x+30=0$

Step-by-step explanation:

Let x = Time taken (in days) by Jean to do the job.

Then, Time taken by Kate to do the job = x-5

Then, together they will take time (t) as

 $\dfrac{1}{t}=\dfrac{1}{x}+\dfrac{1}{x-5}$

$=\dfrac{x-5+x}{x(x-5)}=\dfrac{2x-5}{x(x-5)}$.

$\Rightarrow\ t=\dfrac{x(x-5)}{2x-5}$

Since it is given that Kate and Jean paint a house together in 6 days.

i.e.

$6=\dfrac{x(x-5)}{2x-5}\\\\\Rightarrow 6(2x-5)=x^2-5x\\\\\Rightarrow\ 12x-30=x^2-5x\\\\\Rightarrow\ x^2-5x-12x+30=0\\\\\Rightarrow\ x^2-17x+30=0$

So, the equation represents the time it takes Kate to paint the house by herself is $x^2-17x+30=0$ .