How long would it take Sue to paint the room?

Answer C.

(1) Working with Bob, the project would last 2 hours.
S + B = 2
One equation, two variables. Not sufficient

(2) Bob could accomplish the painting alone in 31⁄4 hours.
B = 31⁄4 hours. Does not say anything about Sue. Not sufficient

Together, you have two distinct equations and two variables. Combined, both are sufficient. Answer C.

Could someone actually go through the problem and solve it?

Sure. I am not sure if statement 2 says 3 1/4 hours or 31/4 hours but I am assuming 31/4 hours

Anyway here is how I would do it:

Given:
\(S + B = 2\)
\(B = 31/4\)

\(\frac{1}{S} + \frac{1}{31/4} = \frac{1}{2}\)

\(\frac{1}{S} + \frac{4}{31} = \frac{1}{2}\)

\(\frac{1}{S} = \frac{1}{2} - \frac{4}{31}\)

\(\frac{1}{S} = \frac{31}{62} - \frac{8}{62}\)

\(\frac{1}{S} = \frac{23}{62}\)

\(S = \frac{62}{23}\)

Would statement 2 say that Bob could accomplish the painting alone in 3 1/4 hours instead of 31/4 hours than the answer would of course change but you can still use the same steps.

Hope this helps.

Thank you very much! I had the same exact process and answer, but was doubting myself. Kudos!

We are asked how long will Sue take to paint the room
basically for solving this question we need to find time required by Sue to complete the task
Statement 1 tells us that working with Bob the task would require 2 hrs
if we consider time required by Bob to complete the task be B hrs and time required by Sue to complete the task be S hrs then
B + S = 2hrs
we don't anything about their individual rate of working so clearly insufficient
Statement 2 tells us Bob alone can complete the task of painting in 31/4 hrs
we don't have info regarding Sue's rate of working so clearly insufficient

Combining both Statements and if we consider time required by Bob to complete the task be B hrs and time required by Sue to complete the task be S hrs then
B + S = 2hrs
B = 31/4 hrs
we can solve this 2 equations(although the time is given you get the idea of solving these 2 equations using principles of time and work)
Correct Answer - C

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