Question

PLEASE HELP!!!! WILL MEDAL AND FAN!!

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. Explain each step.

Answer 1

Allen can complete 1/16 of the project per hour
Brianne can complete 1/18 of the project per hour
Charles can complete 1/x

Together they can accomplish 1/16 + 1/18 + 1/X per hour.
we need a common denominator, which is 288X
=
18x+16x+288/288x

Answer 2

i don't think that answer is correct.

Answer 3

hold on not done

Answer 4

it has to be 1/something, doesn't it?

Answer 5

time=(1)/((1/x)+(1/y))

Answer 6

Choose t as the time it takes them all, so 1/t is the hourly rate.

1/t =
18x+16x+288/288x

Answer 7

or t =
288x/18x+16x+288

Answer 8

gnorris, that answer confuses me. and i know that you got that from searching this question on the internet so i'm not going to medal you <.<

Answer 9

i don't want a metal i was just being nice and trying to help

Answer 10

i understand, but it's really hard for me to get things like this. sorry.

Answer 11

but if you don't want my help I won't help you again sorry to be a bother i'm not good with words i know what to do but cant explain it to you

Answer 12

So, bro, the most important thing to do when tackling these pesky problems is keep in mind that Distance = Rate * Time. You'll see why in a moment.

"Allen can complete a large project in 16 hours." Here, we're presented with a vital piece of information: Allen's TIME. We can already plug this into the Distance = Rate * Time (D = RT) formula. "But what's the distance?" You might ask. Well, Allen's job would be the distance in this case, and how many jobs did he do? Just 1. So our formula now becomes:

D = RT
1 = R(16)
Therefore, R = 1/16. Allen can do 1/16 of his job (the distance) per hour. (this is where the "1/something" comes from. ;D

Applying this exact same reasoning to Brianne, we find that Brianne has a rate of 1/18 job-per-hour.

So now we have the rates. What's our next step? I think it should be to find the times of Brianne and Allen. But we don't have to! Remember, we're looking to find how long these guys take working TOGETHER - this means that they'll both take the same time to complete the project. Just call their time 'x'.

So, applying all that we've learned, we have the following equation for the two hard workers workin' together:

(Rate of Allen)(Time of Allen) + (Rate of Brianne)(Time of Brianne) = Their project

(1/16)(x) + (1/18)(x) = 1

0.11805(x) = 1

x = meh, about 8 and 1/3 hours, I think.