Jon can type 20 pages in 40 minutes, sue can type 20 pages in 30 minutes, and Jack can type 20 pages in 24 min?

Question

Calculate if they worked together, how long would it take all of them to type 20 pages?

Answer 1

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Since all will be typing 20 pages, then the working formula can be simplified to

1/20 + 1/30 + 1/24 = 1/T

Solving for "T"

T = 8 minutes

This is how problems of this type are solved.

HOWEVER, I highly doubt that the answer of T = 8 minutes is really the correct answer. First of all, how do you divide 20 pages among the three? Will Jon start from page 1 to say, page 7? Will Sue start from page 8 to say, page 14? And, will Jack type the rest of the pages?

Anyway, I hope I understood the post correctly.

Answer 2

Lay off Jon and Sue, and give a raise to jack. LOL.

Jon can type 20 pages in 40 minutes.

The pages he would type in a minute = 20/40 = 1/2 pages

sue can type 20 pages in 30 minutes

The pages he would type in a minute = 20/30 = 2/3 pages

Jack can type 20 pages in 24 min

The pages he would type in a minute = 20/24 = 5/6 pages

Therefore the number of pages they would type together in a minute

= 1/2 + 2/3 + 5/6

= 3/6 + 4/6 + 5/6

= 12/6

= 2

So if they type together they would type 2 pages in a minute

Therefore it will take 20/2 minutes, i.e. 10 minutes to type 20 pages if they work together.

Answer 3

Jon types 1/2 page per minute; Sue types 2/3 page per minute, and Jack types 20/24 or 5/6 page per minute. Therefore if they work together, they will produce

(1/2) + (2/3) + (5/6) = 2 pages per minute.

Therefore if they have to produce 20 pages, it will take them 10 minutes.

Answer 4

what if it took all of them to type 20 pages each?? it would take jon 40 min sue 30 min and jack 24

Answer 5

40min-20pg--------1min--20/40pg=1/2pg

30min-20pg---------1min-20/30pg=2/3pg

24min-20pg---------1min-20/24pg

together-----in 1 min---1/2+2/3+20/24

=12/24+16/24+20/24

=48/24=2pg

so 2pg per min

for 20pages total 10 minutes.