Question

Please help guys this is due and I don’t know how to do it :( do any problem you would like, it would help so much!

Answer 1

Answer: 9. 22.5 hours 10. 2 hours 55 minutes 11. 7.5 hours

Explanation:

9.

We take the capacity of the tank as one and the time of filling the tank

with pipe B as x

Hence, the speed of filling the tank with pipe A is 1/15 and the speed of filling the tank with pipe B is 1/x

Thus,

`\displaystyle\\(1)/((1)/(15)+(1)/(x) ) =9\\\\(1)/( (1(x)+1(15))/(15(x)) )=9\\\\(1)/((x+15)/(15x) )=9\\\\(15x)/(x+15) =9\\\\`

Multiply both parts of the equation by (x+15):

15x=9(x+15)

15x=9x+135

15x-9x=9x+135-9x

6x=135

Divide both parts of the equation by 6:

x=22.5 hours

10.

We take the capacity of the tank as one

Hence, the speed of filling the tank with pipe A is 1/7 and the speed of filling the tank with pipe B is 1/5

Thus,

`\displaystyle\\(1)/((1)/(7) +(1)/(5) ) =\\\\(1)/( (1(5)+1(7))/(7(5))) =\\\\(1)/((5+7)/(35) )=\\\\(1)/((12)/(35)) =\\\\(35)/(12)= \\\\2(11)/(12) \ hours=\\\\2\ hours\ 55\ minutes`

11.

We take the unmowed lawn as one and Joshua's lawn mowing time as x

Hence, Brianna's mowing speed is 1/5 and Joshua's mowing speed is 1/x

Thus,

`\displaystyle\\(1)/((1)/(5) +(1)/(x) ) =3\\\\(1)/((1(x)+1(5))/(5(x)) ) =3\\\\(1)/((x+5)/(5x) )=3\\\\(5x)/(x+5)=3`

Multiply both parts of the equation by (x+5):

5x=3(x+5)

5x=3x+15

5x-3x=3x+15-3x

2x=15

Divide both parts of the equation by 2:

x=7.5 hours

Answer 2

Answer: For 9: 22.5 hours

Explanation:

So if pipe A takes 15 hours to fill a tank, then it would fill 1/15 of the tank in a hour. Lets say pipe B fills 1/x of the tank per hour.

Now we make a equation:

1/15 + 1/x = 1/9

Now we solve:

Multiply by the LCM 45(x)

=>3x+45=5x

=>45=2x

=>x=22.5

Pipe B takes 22.5 hours to fill the tank alone.