Respuesta :
To solve this problem you must apply the proccedure shown below:
1. You have that Danny painted the fence in 9 hours faster than Josh. Therefore, let's call:
[tex] x [/tex]: Josh's time
[tex] (x-9) [/tex]: Danny's time
2. In one hour Josh did [tex] \frac{1}{x} [/tex] of the painting job and Danny did [tex] \frac{1}{(x-9)} [/tex]. Working together they did [tex] \frac{1}{7} [/tex] of the painting job. Therefore, you can write the following equation:
[tex] \frac{1}{x}+ \frac{1}{(x-9)} =\frac{1}{7} [/tex]
3. Yes, you have to find the least common denominator to solve for [tex] x [/tex] and solve the equation:
[tex] \frac{(x-9)+x}{x(x-9)} =\frac{1}{7} [/tex]
[tex] 7(2x-9)=x^{2} -9x [/tex]
[tex] x^{2} -23x+63=0 [/tex]
4. When you solve the quadratic equation, you obtain:
[tex] x= 19.82\\ x-9=10.82 [/tex]
The answer is:
Josh: [tex] 19.82 hrs [/tex]
Danny: [tex] 10.82 hrs [/tex]
It would take Danny and josh to paint the fence if each was doing it by himself. Josh x=19.28hrs and Danny=1082hrs
We have given that Danny painted the fence in 9 hours faster than Josh. Therefore
x: Josh's time
x-9: Danny's time
In one hour Josh did 1/x of the painting job and Danny did 1/(x-9). Working together they did 1/7 of the painting job.
Therefore, you can write the following equation
[tex]\frac{1}{x}+\frac{1}{x-9} =\frac{1}{7}[/tex]
Yes, you have to find the least common denominator to solve for and solve the equation
[tex]\frac{(x-9)+x}{x(x-9)} =\frac{1}{7}[/tex]
[tex]7(2x-9)=x^2-9x\\x^2-23x+63=0[/tex]
What is the formula for quadratic equation?
[tex]x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a}[/tex]
We have to solve this quadratic equation
[tex]x^2-23x+63=0\\a=1,b=-23,c=63\\we use the formula \\x=\frac{-b+/-\sqrt{b^{2}-4ac } }{2a} \\x_{1,\:2}=\frac{-\left(-23\right)\pm \sqrt{277}}{2\cdot \:1}\\x_1=\frac{-\left(-23\right)+\sqrt{277}}{2\cdot \:1},x_2=\frac{-\left(-23\right)-\sqrt{277}}{2\cdot \:1}\\x=\frac{23+\sqrt{277}}{2},x=\frac{23-\sqrt{277}}{2}\\\left(\quad x=19.82165\,\:x=3.17834\ \right)[/tex]
we have x=19.82hrs
x-9=19.82-9=10.82hrs
If we take x=3 then x-9 will be negative value and time is always
positive so here we get the contradiction therefore the value of
Therefore we get For Josh x=19.28hrs and
For Danny x-9 =1082hrs.
To learn more about the quadratic equation visit:
https://brainly.com/question/1214333
