Question

Jack can do a job in 2 hours, Tom in 5.
Can someone verify the answer isn't one of the choices?

Answer 1

x x
-- + -- = 1
2 5

Multiply every term by 10

5x + 2x = 10
7x = 10
x = 10/7

x = 1 and 3/7 of an hour.

Answer 2

but 7 isnt a common denominator?

Answer 3

@Blexting - could you explain? this isn't AOPS where everyone understands.

Answer 4

isn't 1/2 + 1/5 = 3/10?

Answer 5

i mean 7/10 oops

Answer 6

OHH i see what i did wrong

Answer 7

i simplified but forgot to use the reciprocal denominator :P damnit

Answer 8

sorry, & thanks

Answer 9

x is the number of hours someone works.

Take Tom... in 1 hour he has done 1/5 of the job.. in 2 hours he has done 2/5 of the job... in 3 hours 3/5 of the job.

We want the job to add to 1 because then you have done "let's say 5/5" of the job which is the whole job.

in 1 hour jack would do 1/2 of the job and Tom 1/5 of the job. which would be 7/10 of the job.

in 2 hours jack would do 2/2 of the job and Tom 2/5 of the job.. which would be 1 2/5.. (Jack would have completed it on his own).

These are always setup the same way

x over (how long it takes for one person) + x over (how long it takes for the other person) = 1

Answer 10

Hrm. Never saw it that way. I just always thought of it through rates, and then just brute forced it. qq

Answer 11

1/2 + 1/5 = 7/10

7 parts get done in 1 hour, and there are a total of 10 parts to do.

after 1 hour, there are still 3 parts to finish up.

60 minutes/7 times 3 = how many minutes?

Answer 12

180/7 = 25.7 is close...

1 hour 25 minutes and a few seconds...

Answer 13

I left it 1 3/7 hours because it matched the multiple choice he was picking from.

Answer 14

thats a good option as well :)