HELP!!!!!!!!!!!!!!!!!!!!!!!!!!

Question

Brian and Ian are decorating sugar cookies, and Alex is sneakily eating the sugar cookies. It takes Brian 2 hours to decorate two dozen cookies by himself, and it takes Ian 5 hours to decorate the same amount. Alex eats 1 cookie every hour and 15 minutes. How long will it take Brian and Ian to decorate two dozen sugar cookies?

Answer 1

IF Alex didn't eat any cookies, working together they'd finish 2 dozen in

1/A + 1/B = 1/X

1/2 + 1/5 = 1/X

multiply by 10X to get

5X + 2X = 10

7X = 10

X = 10/7 = 1 3/7 hours for both to do 2 dozen cookies = about 1.429 hours

but Alex ate one cookie in 1 1/4 hours = 1.25 hours

before they finished that 24th cookie Alex ate one

they do 24 cookies in 1.429 hours when Alex leaves them alone

that's 1 cookie per 1.429/24 = (10/7)/24 = 10/7(24) = 10/168 = 0.059523809 hours = about 3.57 minutes to get an extra cookie to make up for Alex eating one.

So add 1.429 + 0.060 = 1.489 hours = 1 hour and 29 minutes and 20 seconds ,