Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 2

Question

Jonathan can type a 20 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?

Answer 1

That's silly... how can they all type on the same document at once?

Okay, ignoring that for a second... let's express the amount of work each one does in a minute.

Jonathan finishes 1/40 of the document each minute.
Susan finishes 1/30 of the document each minute
Jack finishes 1/24 of the document each minute.

So together they finish 1/40 + 1/30 + 1/24 of the document each minute. If you get a common denominator of 120, you have:
3/120 + 4/120 + 5/120

This works out to 12/120 and reduces to 1/10. So together they finish 1/10 of the document each minute. It will therefore take them 10 minutes to finish it together (assuming they don't get in the way of each other's fingers as they type together...).

Answer 2

You have to start by calculating rates.

Jonathon types 20 pages in 40 minutes or 1/2 page/min
Susan types 20/30 or 2/3 page/min
Jack types 20/24 or 5/6 page/min

Their combined rate is:

1/2 + 2/3 + 5/6

or 3/6 + 4/6 + 5/6 = 12/6 = 2 pages/min

therefore they can type 20 pages in 10 minutes

reality check, the right answer should be less than 25 (jack could do that all by himself) but more than 8 (that would be three jacks typing and the other two are much slower).

looks okay but you should check my problem and my math

10

Answer 3

This is not realistic, they can't work together to type the document efficiently. But if we ignore reality to do the math problem as it is probably intended, this is a "job" problem.

Let
x = time to type document working together

x/40 + x/30 + x/24 = 1 job

Multiplying by the least common multiple 120 we have

3x + 4x + 5x = 120
12x = 120
x = 10 minutes

It will take 10 minutes working together in the unrealistic world of this math problem.

Answer 4

20 pages

Jonathan: 2 minutes per page
Susan: 1.5 minutes per page
Jack: 1.2 minutes per page

After 6 minutes, Jonathan has typed 3 pages, Susan 4 pages, and Jack 5 pages (12 pages total)

After 10 minutes, Jonathan has typed 5 pages, Susan 6 2/3 pages, and Jack 8 1/3 pages for a total of 20 pages.

It takes 10 minutes working together.

Answer 5

(1/40)t + (1/30)t + (1/24)t = 1
t = 10 minutes

break it down into how much each person can do in 1 minute. It equals 1 because thats how many documents they are working on.

Answer 6

this is math B 2/3 stuff....I forgot how to solve it, its stuff that I'm going to learn next term