SOLUTION: Theresa can do a piece of work in 15 days. After she has worked 3 days, Rowena joins her and they finish work in 4 days. How long can Rowena finish the work alone?

Question 1172530: Theresa can do a piece of work in 15 days. After she has worked 3 days, Rowena joins her and they finish work in 4 days. How long can Rowena finish the work alone?
Found 3 solutions by VFBundy, greenestamps, josgarithmetic:
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
After 3 days, Theresa has completed 3/15 (or 1/5) of the work. This means there is 4/5 of the work remaining.

So, working together, Theresa and Rowena can complete 4/5 of the work in 4 days.

Theresa's rate of work is: 1/15 of the work per day.

Rowena's rate of work is: 1/x of the work per day.

Rate of both working together: 1/15 + 1/x = x/15x + 15/15x = (x + 15)/15x of the work per day.

Rate of Work TIMES Days of Work = Total work

[(x + 15)/15x] * 4 = 4/5

4(x + 15)/15x = 4/5

(4x + 60)/15x = 4/5

5(4x + 60) = 4(15x)

20x + 300 = 60x

-40x = -300

x = 15/2

That means it would have taken Rowena 15/2 days (or, 7.5 days) to do the ENTIRE work alone. However, since 1/5 of the work was already done by Theresa, only 4/5 of the work remains. That means it will take Rowena (4/5 * 15/2) days to FINISH the work alone. 4/5 * 15/2 = 60/10 = 6. Therefore, it will take Rowena 6 days to finish the remaining work alone.

**NOTE: The question specifically asks how long it will take Rowena to FINISH the work, implying it is asking how long it will take her to complete the work AFTER the work by Theresa has already been done.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Theresa working alone for 3 days completes 3/15 = 1/5 of the job; 4/5 of the job remains to be done.

Theresa and Rowena together complete those 4/5 of the job in 4 days; that means together they complete 1/5 of the job each day.

Each day Theresa alone does 1/15 of the job and together they do 1/5 of the job. That means each day Rowena does 1/5-1/15 = 3/15-1/15 = 2/15 of the job.

Since Rowena does 2/15 of the job each day, the number of days it would take Rowena to do the whole job alone is 15/2, or 7 1/2.

ANSWER: 7 and a half days

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Therasa's rate, .
Rowena's rate, .
Combined rate of both, .

Question based on 1 job.

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