Question

@matricked Hayden is a manager at a landscaping company. He has 3 workers to landscape an entire park, Cody, Kaitlyn, and Joseph. Cody can complete the project in 8 hours. Kaitlyn can complete the project in 6 hours. Joseph is new, so no one knows how long it will take him.

Hayden assigns all of them to complete the park together. Explain to Hayden how this project can tell him how long it would take Joseph to complete the project if he worked by himself. Use complete sentences.

Answer 1

I set up the ratios.

1/8 + 1/6 + 1/x = ?
I have no idea where to go from here. Start by finding the LCD, perhaps?

Answer 2

yup

Answer 3

Okay. We'd have 24x, right?

Answer 4

3x + 4x + 24

Answer 5

assum the total work to be completed in y hr
then we have
1/8 + 1/6 + 1/x = 1/y
7/24 +1/x=1/y

Answer 6

1/x = 1/y -7/24
1/x = (24-7y)/24y
x= 24y/(24-7y)

Answer 7

Aaah...hold on

Answer 8

they meant to make x as the subject of the formula
once the y (time of completion of the project is known) we may know x

Answer 9

Okay, so we shouldn't include x as the common denominator. Gotchya.

Answer 10

but here
24-7y >0

Answer 11

Can you pause for a second? How did you get this part? 1/x = (24-7y)/24y
I got up to 1/x = 1/y - 7/24

Answer 12

I can see cross multiplying to get 24 - 7y...I don't get the denominator of 24y

Answer 13

1/y - 7/24
LCM of y and 24 is 24y and hence further

Answer 14

Got it! Thanks!

Answer 15

yw

Answer 16

Why was it flipped when you divided by 1?

Answer 17

1/ (1/a) = a

Answer 18

It...canceled? I'm sorry, I'm lost. So brain dead :p

Answer 19

1/1 * a/1 =a

Answer 20

Okay, I kind of get that. Can we simplify this any more?

Answer 21

Thank you so so so much for helping me. I had to finish my class tonight and I've been working for so long I was about to fall asleep on my laptop, haha. You were a life saver.

Answer 22

yw

Answer 23

Anything else need to be done here? @matricked

Answer 24

is the question asking anything further...