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August 6th, 2012, 05:20 AM   #1
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Problem with Direct and Inverse Variation

A and B can do a job in 12 days. After working for two days. they are assisted by C, who works at the same rate as A. The work takes 6 1/4 (Six, 1 by 4th) days more to finish. In how many days will B alone do the work?

Please help
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August 6th, 2012, 09:51 AM   #2
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Re: Problem with Direct and Inverse Variation

Giving you the solution may be nice (to you!) but will not really HELP you.

Here's an example, where the "job" is picking 840 apples, A picking @ 20 per minute, B picking @ 15 per minute:
After 2 minutes (2 days in your case), apples left to be picked = 840 - 2(20)(15) = 770

C now arrives, picking @ 20 (same as A), so combined speed = 20 + 15 + 20 = 55 apples per minute.
Time to complete job = 770 / 55 = 14 minutes.

Now, using that as a "guide", let's see YOUR stuff
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August 7th, 2012, 07:41 AM   #3
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Re: Problem with Direct and Inverse Variation

Using my example, problem can be worded this way (yours too!):
A and B travel distance k miles at combined speed a+b in 24 hours.
If, after 2 hours, A doubles speed, then remainder can be travelled in 14 hours.
If B travelled alone, how long would it take him to travel the k miles?

And you'd be able to "see" clearly what's "happening":
Code:
At combined speeds, distance k miles is travelled in 24 hours:
@(a + b)mph
------------------------------k miles---------------------------------> 24 hours

So: k / (a + b) = 24 ; simplify to get:
a = (k - 24b) / 24 [1]

After 2 hours, A doubles his speed; remaining distance travelled in 14 hours:
@(a + b)mph                   @(2a + b)mph
----2(a + b) miles---->2 hours---------------k - 2(a + b) miles-------> 14 hours

So: (k - 2(a + b)) / (2a + b) = 14 ; simplify to get: 
30a + 16b = k [2]
Substitute [1] in [2]:
30[(k - 24b) / 24] + 16b = k ; simplify to get:
b = k / 56
So B's speed is k/56, therefore takes 56 hours if alone.

Yours would be:
A and B travel distance k miles at combined speed a+b in 12 hours.
If, after 2 hours, A doubles speed, then remainder can be travelled in 25/4 hours.
If B travelled alone, how long would it take him to travel the k miles?
OK?

By the way, you could use distance 1 (k = 1) and get 1/speed (1/56 in my example).
And that's usually how these are solved; like: in 1 hour, A and B combined do 1/12 of job.
BUT I simply hate to use that way when trying to show someone for first time.
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August 8th, 2012, 05:11 PM   #4
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Re: Problem with Direct and Inverse Variation

Thank You!!
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August 8th, 2012, 06:50 PM   #5
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Re: Problem with Direct and Inverse Variation

I would turn the statement "A and B can do a job in 12 days" into the equation:



After A and B work for two days, 5/6 of the job is left to do. Then we are told. "they are assisted by C, who works at the same rate as A" which means C = A. And the statement "The work takes 6 1/4 days more to finish" gives us:



Solving the two equations gives:



Therefore, it would take B 30 days to complete the job working alone.
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A and B can do a job in 12 days. After working for two days, they are assisted by C, who works at the same rate as A. The work takes 6 1/4 days more to finish. In how many days will B alone do the work?
,
A and B can do a job in 12 days .after working for two days ,they are assisted by C,who works at the same rate as A.the wirks takes 25/4 days more to finish .in how many days will B alone do the works
,

A and B can do a job in 12 days. after working for two days, they are assisted by C, who works at the same rate as A.The works 25/4 days more to finish. In how many days will B alone do the works.

,

A and B can do a job in 12 days .after working for two days,they assisted by C , who works at same rate as A .the works takes 25/4 days moreto finish. In how many days will B alone do the work?

,

A and B can do a job in 12 days. after working for two days, they are assisted by C, who works at the same rate as A.The works 25/4 days more to finish. In how many days will B alone do the works.

,

a and b can do a work in 12 days. After working for 2 days they were assisted by Claire, who works at the same rate as A. The work takes 6 1/4 days more to finish. In how many days will B alone do the work?

,

A and B can do a job in 12 days.after working for 2 days,they are assisted by C,who works at the same rate as A.the work takes 25/4 days more to finish.in how many days will B alone do the work

,

A and B can do a job in 12 days. after working for two days, they are assisted by C, who works at the same rate as A.The works 25/4 days more to finish. In how many days will B alone do the works.

,

A and B can do a job in 12 days. after working for two days, they are assisted by C, who works at the same rate as A.The works 25/4 days more to finish. In how many days will B alone do the works.

,

A and B can do a job in 12 days. after working for two days, they are assisted by C, who works at the same rate as A.The works 25/4 days more to finish. In how many days will B alone do the works.

,

A and B can do a job in 12 days. After working for two days they are assisted by c who work at the same rate as A.

,

a and b can do the job in 12 days. after working for two days.they are assisted c .who works at the same rate as a. they works 25/4 days to finish. in how many days will be alone do the work

,

A and B can do a job in 12 days. After working 2 days, they are assisted by C, who works at the same rate as A. The work takes

,

A and B can do a job in 12 days. after working for two days ,they are assisted by C,who works at the same rate as A.the work takes 25/4 days more to finish .in how many days will B alone do the work?

,

a & b can do a job in 12 days.after working for two days,they are assisted by C,who works at the same rate as. A.The work takes 25/4 days

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