Question

PLEASE HELP!!!

Joselyn is a manager at a sign-painting company. She has two painters, Allen and Brianne. Allen can complete a large project in 16 hours. Brianne can complete the project in 18 hours. Joselyn wants to know how long it will take them to complete the project together.

Write an equation and solve for the time it takes Allen and Brianne to complete the project together.

Answer 1

@nincompoop

@hartnn

Answer 2

Let them take 'x' hours to complete the work by working together.

Answer 3

` Allen can complete a large project in 16 hours`
if Allen works alone, how much of the work she can complete in 1 hour?

Answer 4

1/16 of the project?

Answer 5

yes!
what about Brianne?

Answer 6

1/18

Answer 7

yes,
what if they work together?

Answer 8

um, 1/16 + 1/18

Answer 9

?

Answer 10

good!

now we know they both can do the entire work in 'x' hours by working together,
we can say that they both will complete 1/x of the work in one hour.
makes sense?

Answer 11

yes

Answer 12

and we already know they both can complete it in 1/16 +1/18 of the work in 1 hr.

so we can equate:
\(\Large \dfrac{1}{16} + \dfrac{1}{18} =\dfrac{1}{x}\)

can you isolate x from here?

Answer 13

um 1/x = 17/144 ?

Answer 14

bdw, this is the equation they want :
\(\Large \dfrac{1}{16} + \dfrac{1}{18} =\dfrac{1}{x}\)

now you're solving for the time,
yes,
1/x= 17/144
so,

x = 144/7

Answer 15

x= 144/17**

Answer 16

ok. what's next?

Answer 17

it will take them 144/17 or 8.47 hrs if they work together.
and thats it!

Answer 18

ok thank you :)

Answer 19

welcome ^_^