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

x^2 − 7x − 30 = 0

Explanation:

Answer 2

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

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

`(1)/(t)=(1)/(x)+(1)/(x-5)`

`=(x-5+x)/(x(x-5))=(2x-5)/(x(x-5))`.

`\Rightarrow\ t=(x(x-5))/(2x-5)`

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

i.e.

`6=(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` .