Question

Elissa can do a job in 5 hours. Elissa and Lori working together can do the same job in 2 hours. How long would it take Lori to do the job alone?

Answer 1

i got 4 2/3 hours

Answer 2

Rate of Elissa is 1/5 ; let the rate of Lori be 1/x .

Now 1(1/5) + 1/(1/x) = 2 ; find x .

Answer 3

It should be 1/(1/5)

Answer 4

that doesnt make sense. I tried again and got 2 2/3 hours

Answer 5

helpp?!!

Answer 6

you are solving
\[\frac{1}{5} + x = \frac{1}{2}\]
\[x = \frac{1}{2} - \frac{1}{5} = \frac{5}{10} - \frac{2}{10} = \frac{3}{10}\]
the rate is 3/10
therefore time is 10/3

Answer 7

3 1/3 hours?

Answer 8

Elissa's rate (\(R_E\)) is 1 job / 5 hours, or 1/5 jobs/hour. Elissa + Lori working together have a rate (\(R_E+R_L\)) of 1 job /2 hours, or 1/2 jobs/hour. You want to find Lori's rate (\(R_L\)).

Standard rate formula is \(w = rt\) where \(w\) is work done, \(r\) is rate, \(t\) is time. For 1 job, \(w=1\). \(r = R_E+R_L\). \(t = 2\).

\[1 = (R_E+R_L)(2)\]Substitute known value for \(R_E\):\[1=(\frac{1}{5}+R_L)(2)\]Multiply through by 5
\[5=2+10R_L\]\[3=10R_L\]\[R_L = 3/10\]

So, for Lori to do it alone:
\[1 = R_L*t\]\[1=(3/10)t\]\[t=10/3 = 3\frac{1}{3}\]

Answer 9

@oholmes : Focus on the word "alone" , not together .

Answer 10

Checking the work:

if Lori takes 3 1/3 hours to do the whole job herself, in 2 hours she will accomplish \[\frac{2}{3 \frac{1}{3}} = 6/10\] of the job. If Elissa takes 1 hour to do 1/5 of a job, in 2 hours she will do 2/5 of the job. In two hours together, they will have done 6/10 + 2/5 = 6/10 + 4/10 = 10/10 or all of the job. The answer is correct.

Answer 11

Figure out the individual rate for each worker, pump, drain, machine, etc. Then combine them as specified by the problem statement and you should get the right answer.