Working together, Max and Mandy painted the living room in

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Working together, Max and Mandy painted the living room in six hours. How long would it have taken for Max to paint the room by himself?

1) Mandy paints twice as fast as Max does.
2) If Max had left when the job was half-finished, it would have taken Mandy hours \(4\frac{1}{2}\) to finish the job by herself.

The OA is D

Source: Princeton Review
Source: — Data Sufficiency |

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by joao_cardoso123 » Sun Nov 10, 2019 9:35 am
initially we know that their painting speeds combined are equal to 1room/6h
which can be written as y+x=1/6 (where y is Mandy's speed, x is Max's speed, and the units are "rooms painted per hour")

condition (1) alone can give the answer:
we can re-write the equation as 2x+x=1/6 or x=1/18; Max would take 18h to paint the room

condition (2) alone can give the answer:
Mandy would take 4.5h to paint half a room: Mandy's speed is 1room/9h
this tells us that 1/9+x=1/6, where x is Max's speed
x=1/6-1/9=3/18-2/18=1/18; Max would take 18h to paint the room