Help with a Compass practice question

[mathmigrainia]

I am practicing for the Compass Test and I have a problem with one of the test questions.

"If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

A. 2 hours and 24 minutes
B. 3 hours and 12 minutes
C. 3 hours and 44 minutes
D. 4 hours and 10 minutes
E. 4 hours and 33 minutes "
copied from
http://www.testprepreview.com/modules/algebra1c.htm

I have been working on this problem for a long time, If this were the real test I would have got it right, but the minutes part of the answer is way off from my answer. Would someone please help me figure out how to get this exactly right? I do ok with the rest of the test but this really bothers me since numbers are supposed to be exact and I cannot come up with the exact number. Thanks a lot for your help this is my first post.

 

[Loren]

I assume you got an answer of 2.4 hours.
Your job becomes converting .4 hours to so many minutes.
\(\displaystyle .4\ hour \times \frac{60\ min}{1 hour} = .4 \times 60\ min = 24\ min.\)

Notice that the fraction (60 min)/(1 hour) = 1. So, your are multiplying the hours by 1 which does not change its value. Notice also, that the hours cancel.

 

[Denis]

Relax!
Sally: 4 hours; so 1/4 of job in 1 hour
John: 6 hours; so 1/6 of job in 1 hour

Together, in 1 hour: 1/4 + 1/6 = 5/12 of job

5/12 = 1 hour
full = 12/5 = 2 2/5 hours = 2 hours 24 minutes ; kapish?

 

[mathmigrainia]

Relax!
Sally: 4 hours; so 1/4 of job in 1 hour
John: 6 hours; so 1/6 of job in 1 hour

Together, in 1 hour: 1/4 + 1/6 = 5/12 of job

5/12 = 1 hour
full = 12/5 = 2 2/5 hours = 2 hours 24 minutes ; kapish?

I am with you until you get to "full = 12/5 = 2 2/5 hours = 2 hours 24 minutes"

I don't know what that means.


Also

I assume you got an answer of 2.4 hours.
Your job becomes converting .4 hours to so many minutes.
\(\displaystyle .4\ hour \times \frac{60\ min}{1 hour} = .4 \times 60\ min = 24\ min.\)

Notice that the fraction (60 min)/(1 hour) = 1. So, your are multiplying the hours by 1 which does not change its value. Notice also, that the hours cancel.

I did not get 2.4 hours I got 2 hours and 10 minutes how did you get 2.4 hours?

This is the way I solved or (didn't) solve it.
1/4 +1/6 = 5/12
so 5/12 + 5/12 =10/12 so in 2 hours they would have complete 10/12 of the house. That would leave 2/12 of the house to be completed by both of them which is 2/12 of 60 or 2/12x60= 10 minutes. Please tell me where I went wrong logically because I am not getting it. Thanks for your help though.

 

[Denis]

This is the way I solved or (didn't) solve it.
1/4 +1/6 = 5/12
so 5/12 + 5/12 =10/12 so in 2 hours they would have complete 10/12 of the house. That would leave 2/12 of the house to be completed by both of them which is 2/12 of 60 or 2/12x60= 10 minutes. Please tell me where I went wrong logically because I am not getting it.

Once more, RELAX!
Yes, 2/12 (or 1/6) of the house is left after 2 hours: good job.
BUT that's 2/12 of the HOUSE, not 2/12 of 1 hour...see that?

We know that 5/12 of house takes 60 minutes, so 1/12 takes 60/5 = 12 minutes, right?
So 2/12 = 24 minutes...OK?

 

[mathmigrainia]

This is the way I solved or (didn't) solve it.
1/4 +1/6 = 5/12
so 5/12 + 5/12 =10/12 so in 2 hours they would have complete 10/12 of the house. That would leave 2/12 of the house to be completed by both of them which is 2/12 of 60 or 2/12x60= 10 minutes. Please tell me where I went wrong logically because I am not getting it.

Once more, RELAX!
Yes, 2/12 (or 1/6) of the house is left after 2 hours: good job.
BUT that's 2/12 of the HOUSE, not 2/12 of 1 hour...see that?

We know that 5/12 of house takes 60 minutes, so 1/12 takes 60/5 = 12 minutes, right?
So 2/12 = 24 minutes...OK?

Thanks Denis and Loren I finally got it, it seems so simple now.