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Combined rate formula?

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Combined rate formula? [#permalink] New post 18 Jun 2013, 22:24
I remember having seen a formula for rates

\frac{A*B}{A+B} but I can't remember what it is for (if anything at all). Can someone clarify this for me?

Thanks
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Re: Combined rate formula? [#permalink] New post 19 Jun 2013, 00:09
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Skag55 wrote:
I remember having seen a formula for rates

\frac{A*B}{A+B} but I can't remember what it is for (if anything at all). Can someone clarify this for me?

Thanks


hi,

If A can finish a work in X time and B can finish the
same work in Y time then both of them together can
finish that work in (X*Y)/ (X+Y) time.

If A can finish a work in X time and A & B together can
finish the same work in S time then B can finish that
work in (XS)/(X-S) time.

If A can finish a work in X time and B in Y time and C in
Z time then all of them working together will finish the
work in (XYZ)/ (XY +YZ +XZ) time

kudos if it helped
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Re: Combined rate formula? [#permalink] New post 19 Jun 2013, 01:13
shaileshmishra wrote:
Skag55 wrote:
I remember having seen a formula for rates

\frac{A*B}{A+B} but I can't remember what it is for (if anything at all). Can someone clarify this for me?

Thanks


hi,

If A can finish a work in X time and B can finish the
same work in Y time then both of them together can
finish that work in (X*Y)/ (X+Y) time.

If A can finish a work in X time and A & B together can
finish the same work in S time then B can finish that
work in (XS)/(X-S) time.

If A can finish a work in X time and B in Y time and C in
Z time then all of them working together will finish the
work in (XYZ)/ (XY +YZ +XZ) time

kudos if it helped


...kudos if it deserves it.

Though I think it does, cause it covers more than I asked and it's nicely laid out! :)
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Re: Combined rate formula? [#permalink] New post 19 Jun 2013, 01:16
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Skag55 wrote:
I remember having seen a formula for rates

\frac{A*B}{A+B} but I can't remember what it is for (if anything at all). Can someone clarify this for me?

Thanks


THEORY
There are several important things you should know to solve work problems:

1. Time, rate and job in work problems are in the same relationship as time, speed (rate) and distance in rate problems.

time*speed=distance <--> time*rate=job \ done. For example when we are told that a man can do a certain job in 3 hours we can write: 3*rate=1 --> rate=\frac{1}{3} job/hour. Or when we are told that 2 printers need 5 hours to complete a certain job then 5*(2*rate)=1 --> so rate of 1 printer is rate=\frac{1}{10} job/hour. Another example: if we are told that 2 printers need 3 hours to print 12 pages then 3*(2*rate)=12 --> so rate of 1 printer is rate=2 pages per hour;

So, time to complete one job = reciprocal of rate. For example if 6 hours (time) are needed to complete one job --> 1/6 of the job will be done in 1 hour (rate).

2. We can sum the rates.

If we are told that A can complete one job in 2 hours and B can complete the same job in 3 hours, then A's rate is rate_a=\frac{job}{time}=\frac{1}{2} job/hour and B's rate is rate_b=\frac{job}{time}=\frac{1}{3} job/hour. Combined rate of A and B working simultaneously would be rate_{a+b}=rate_a+rate_b=\frac{1}{2}+\frac{1}{3}=\frac{5}{6} job/hour, which means that they will complete \frac{5}{6} job in one hour working together.

3. For multiple entities: \frac{1}{t_1}+\frac{1}{t_2}+\frac{1}{t_3}+...+\frac{1}{t_n}=\frac{1}{T}, where T is time needed for these entities to complete a given job working simultaneously.

For example if:
Time needed for A to complete the job is A hours;
Time needed for B to complete the job is B hours;
Time needed for C to complete the job is C hours;
...
Time needed for N to complete the job is N hours;

Then: \frac{1}{A}+\frac{1}{B}+\frac{1}{C}+...+\frac{1}{N}=\frac{1}{T}, where T is the time needed for A, B, C, ..., and N to complete the job working simultaneously.

For two and three entities (workers, pumps, ...):

General formula for calculating the time needed for two workers A and B working simultaneously to complete one job:

Given that t_1 and t_2 are the respective individual times needed for A and B workers (pumps, ...) to complete the job, then time needed for A and B working simultaneously to complete the job equals to T_{(A&B)}=\frac{t_1*t_2}{t_1+t_2} hours, which is reciprocal of the sum of their respective rates (\frac{1}{t_1}+\frac{1}{t_2}=\frac{1}{T}).

General formula for calculating the time needed for three A, B and C workers working simultaneously to complete one job:

T_{(A&B&C)}=\frac{t_1*t_2*t_3}{t_1*t_2+t_1*t_3+t_2*t_3} hours.

Some work problems with solutions:
time-n-work-problem-82718.html?hilit=reciprocal%20rate
facing-problem-with-this-question-91187.html?highlight=rate+reciprocal
what-am-i-doing-wrong-to-bunuel-91124.html?highlight=rate+reciprocal
gmat-prep-ps-93365.html?hilit=reciprocal%20rate
questions-from-gmat-prep-practice-exam-please-help-93632.html?hilit=reciprocal%20rate
a-good-one-98479.html?hilit=rate
solution-required-100221.html?hilit=work%20rate%20done
work-problem-98599.html?hilit=work%20rate%20done
hours-to-type-pages-102407.html?hilit=answer%20choices%20or%20solve%20quadratic%20equation.%20R

Theory on work/rate problems: work-word-problems-made-easy-87357.html

All DS work/rate problems to practice: search.php?search_id=tag&tag_id=46
All PS work/rate problems to practice: search.php?search_id=tag&tag_id=66


Hope it helps.
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Re: Combined rate formula? [#permalink] New post 19 Jun 2013, 01:19
Thanks Bunuel, helpful and thorough as always!
Re: Combined rate formula?   [#permalink] 19 Jun 2013, 01:19
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