Brain Teasers
Painting the Faculty Room
Fun: (2.21)
Difficulty: (2.35)
Puzzle ID: #32767
Submitted By: moonsliver86 Corrected By: dalfamnest
Submitted By: moonsliver86 Corrected By: dalfamnest
The Math Department wanted to surprise Dean TJ by painting the Faculty Room pink.
It is known that Prof. Jaime, the Geometry teacher, and Prof. Basil, the Algebra teacher, can paint the room in 12 days.
On the other hand, Prof. Wilhelm, the Calculus teacher, and Prof. Nichel, the Trigonometry teacher, can paint the room in 16 days.
If Jaime and Wilhelm can finish painting the room in only 8 days, how long will it take Nichel and Basil to finish painting the room?
It is known that Prof. Jaime, the Geometry teacher, and Prof. Basil, the Algebra teacher, can paint the room in 12 days.
On the other hand, Prof. Wilhelm, the Calculus teacher, and Prof. Nichel, the Trigonometry teacher, can paint the room in 16 days.
If Jaime and Wilhelm can finish painting the room in only 8 days, how long will it take Nichel and Basil to finish painting the room?
Hint
Nichel and Basil don't like each other very much.Answer
Let us first set our variables:J - Jaime's rate
B - Basil's rate
W - Wilhelm's rate
N - Nichel's rate
We are given that:
(1) J + B = 1/12
(2) W + N = 1/16
(3) J + W = 1/8
We are asked to look for B+N.
Note that:
J+B+W+N=J+W+B+N
(J+B)+(W+N)=(J+W)+(B+N)
1/12 + 1/16 = 1/8 + (B+N)
(B+N) = 1/48
Therefore, it would take Nichel and Basil 48 days to finish painting the room.
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Comments
Whoa, how big is this faculty room? And why is the faculty going to paint it?
Am I missing something? By my observation, Basil could paint tye room by himself in 24 days and Nigel could do it in 32 Why would it take 48 for 2 of them? I'm confused.
Never mind. I see the error of my ways.
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