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Martha can rake the leaves i her yard in 2 hours. Her younger brother can do the job in 6 hours. How long will it take them to the job if they worked together? I know the answer is 3/2 but i dont really understand how this answer was gotten

Question

WILL STAR & FAN! 
Martha can rake the leaves i her yard in 2 hours. Her younger brother can do the job in 6 hours. How long will it take them to the job if they worked together? I know the answer is 3/2 but i dont really understand how this answer was gotten

anonymous · Answer

So the problem says Martha rakes the leaves in 2 hours, and her younger brother does it in 6.

anonymous · Answer

You want to see the amount of time it takes if they both raked leaves at the same time

anonymous · Answer

yes

anonymous · Answer

her brother takes 3 times longer than Martha to rake the leaves.

anonymous · Answer

so if M equals Martha, 3M=M

anonymous · Answer

both added together is 8 so i retriceued dividing by 2 lol

anonymous · Answer

oops, not 3M equals M. 3M equals her brother

anonymous · Answer

but i catch your drift so 2*3=6

anonymous · Answer

wait, now im messing up, hold on, I'll rewrite it

anonymous · Answer

take your time :)

anonymous · Answer

sorry, the post button disappeared for some reason

anonymous · Answer

Martha takes 2 hours
Her brother takes 6 hours
Lets say Martha equals M and her brother equals B

anonymous · Answer

great, im making it too complex now

anonymous · Answer

lmao im a lil confused. but how does the answer end up being 3/2 hours then?

anonymous · Answer

how did you get 3/2?

anonymous · Answer

my brain isn't working right now...

anonymous · Answer

Got it! martha takes 2 hours, so in 1 hour she rakes 1/2 of the leaves

anonymous · Answer

her brother takes 6 hours, so in 1 hour her brother rakes 1/6 of the leaves

anonymous · Answer

x/2 + x/6 = 1

x is hour

anonymous · Answer

3/2 is the in the answer key

anonymous · Answer

ok but what would have to be added together?

anonymous · Answer

cause 1/2 + 1/6 is 2/3 not 3/2 thats one of the answer choices to trick me tho

anonymous · Answer

theres a few steps before that, its not simple addition

anonymous · Answer

basically, x/2 + x/6 equals (1/2 + 1/6) times X

anonymous · Answer

so that would make it (1/2 + 1/6) * X = 1

anonymous · Answer

so 2/3 times x = 1

anonymous · Answer

ohhhhh ok. so when you divide 1 by a fraction you flip it?

anonymous · Answer

you basically solve for x after that, since X is the amount of time it took to rake the leaves

anonymous · Answer

thanks :) got it