Question

CHECK MY WORK PLEASE? :)
the question is:

Joselyn is a manager at a sign painting company. She has three painters, Allen, Brianne, and Charles. Allen can complete a large project in 16 hours. Brianne can complete the same sized project in 18 hours. Charles is new, so no one knows how long it will take him.

Joselyn assigns them all a large project to complete together. Explain to Joselyn how this project can tell her how long it would take Charles if he worked by himself. Use complete sentences.

Answer 1

I'll post my answer now

Answer 2

its correct so far.

Now ask Joselyn to note down the time taken to complete the work when all of them did together.

Let that time be y hours.

Answer 3

I used t to represent the time it would take in hours, is that alright?

Answer 4

yes, we can use any variable, lets say t

so Joselyn knows 't'
and can find the 'x'
using the equation.
\(\dfrac{1}{16}+\dfrac{1}{18}+\dfrac{1}{X} = \dfrac{1}{t}\)

Answer 5

would that suffice, or you want to isolate X?

Answer 6

Ohh, yes I understand! Once she gathers the amount of time, wouldn't we need to isolate it?

Answer 7

once t is known,

to solve for X,
it needs to be isolate.

whether you do it now or after getting the value of t

Answer 8

Okay so in order to isolate it, we need to divide the 1 by itself? I'm a bit confused in this part

Answer 9

ok, to isolate X,

bring all X terms on one side.

so you can shift +1/X on the right side and +1/t to the left

Answer 10

Right because there is only one x term! that makes sense. is there anything else I would need to do? I was going to say to add 1/16 and 1/18 but that just seems incorrect especially if the + 1/t is there

Answer 11

still we have 1/X on the right and not X!

so yeah, add 1/16 and 1/18 first.

then we'll see what we can do with 1/t

Answer 12

Alright, wouldn't adding the fractions give us 17/144 ?

Answer 13

good

17/144 +1/t = 1/X

cross-multiplication :)

a/b +c/d = (ad+bc)/bd

Answer 14

Sorry for all the questions haha, these are just review questions and I haven't studied this in ages! Just now I'm refreshing my memory :)

Answer 15

yes