Word problem

**Baffz** · November 17th 2010, 11:12 AM

so i missed this lesson and i cant seem to figure out what to do, ill just simplify the word problem....basically.

person 1 complete job in m-5 minutes
person 2 completes the job in m minutes
person 3 completes the job in same amount of time as person 2
together they take 3.23 minutes to complete the job... how long does person 2 take to finish the job?

tanks in advance

**Unknown008** · November 17th 2010, 11:25 AM

You use this formula:

$\dfrac{1}{t_1} + \dfrac{1}{t_2} + \dfrac{1}{t_3} = \dfrac{1}{t_{total}}$

Can you give it a try?

**Baffz** · November 17th 2010, 03:11 PM

i tried about 5 times and i cant seem to get the right answer. im thinking the answer at the back of the book is wrong. can someone give it a try?

**bjhopper** · November 17th 2010, 04:18 PM

Hi baffz,
Substitute the values in the given equation t1 = 5 , t2 =m, t3 = m and the sum =1/3.23 and yes 2 and 3 are slow workers

bjh

**Baffz** · November 17th 2010, 04:36 PM

wouldnt i sub in m-5 into t1?

**Soroban** · November 17th 2010, 05:07 PM

Hello, Baffz!

$\text{Person }A\text{ completes the job in }m-5\text{ minutes.}$
$\text{Person }B\text{ completes the job in }m\text{ minutes.}$
$\text{Person }C\text{ completes the job in }m\text{ minutes.}$
$\text{Together they complete the job in 3.23 minutes.}$

$\text{How long does person }B\text{ take to complete the job alone?}$

Here is the reasoning behind that mysterious equation . . .

Person $\,A$ does the job in $m-5$ minues.
. . In one minute, he can do $\frac{1}{m-5}$ of the job.
(Note that $\,m \,>\,5$ )

Person $\,B$ does the job in $\,m$ minutes.
. . In one minute, he can do $\frac{1}{m}$ of the job.

Person $C$ does the job in $\,m$ minutes.
. . In one minute, he can do $\frac{1}{m}$ of the job.

Working together for one minute, they can do: . $\frac{1}{m-5} + \frac{1}{m} + \frac{1}{m}$ of the job. .[1]

We are told that, working together, they do the job is 3.23 minutes.
. . In one minute, they can do $\frac{1}{3.23}$ of the job. .[2]

We just described the amount of work done in one minute in two ways.

Equate [1] and [2]: . $\displaystyle \frac{1}{m-5} + \frac{1}{m} + \frac{1}{m} \;=\;\frac{1}{3.23}$

. . There is our equation!

Multiply by $3.23m(m-5)\!:$

. . $3.23m + 3.23(m-5) + 3.23(m-5) \:=\:m(m-5)$

This simplifies to: . $m^2 - 14.69m + 32.3 \:=\:0$

Quadratic Formula:

. . $\displaystyle m \;=\;\frac{14.69 \pm \sqrt{14.69^2 - 4(1)(32.3)}}{2(1)} \;=\;\frac{14.69 \pm \sqrt{86.5961}}{2}$

. . . . . $=\;\dfrac{14.69 \pm 9.305702553}{2} \;=\;\begin{Bmatrix} 2.692148724 \\ 11.99785128 \end{Bmatrix}$

Take the larger value: . $m \:\approx\:12$

Working alone, person $\,B$ would take 12 minutes to do the job.

**bjhopper** · November 17th 2010, 05:46 PM

Sorry baffz I misread the time for person 1 .It would have been clearer if the times for each were expressed in t and t-5

bjh

**Baffz** · November 17th 2010, 05:47 PM

thanks soroban thats the correct answer but im not understanding why i multiply by 3.23m(m-5)?

EDIT: is it because those are the denominators?

**Unknown008** · November 17th 2010, 07:51 PM

Yes, to remove all the fractions.

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