codeblue wrote:
Bunuel wrote:
Official Solution:
Statement (1) by itself is sufficient. S1 reduces to equation \(\frac{1}{J} + \frac{1}{2J} = \frac{1}{4}\), where \(J\) denotes the time it takes Jack to paint the wall alone. From this equation, \(J = 6\).
Statement (2) by itself is sufficient. S2 reduces to equation \(\frac{1}{J} + 2*(\frac{1}{4} - \frac{1}{J}) = \frac{1}{3}\), where \(\frac{1}{4} - \frac{1}{J}\) is Tom's actual painting speed. From this equation, \(J = 6\).
Answer: D
For statement 2, I think the correct equation is 1/J + 2(1/4 - 1/J) = 1/3
That would yield J = 6.. what am I doing wrong here? Substituting equation for Tom into the given statement and solving..
You have the same equation as above.
Alternative explanation:
If working together, brothers Tom and Jack can paint a wall in 4 hours, how much time would it take Jack to paint the wall alone?Say the
rates of Tom and Jack are T job/hour and J job/hour, respectively. Their combined rate is T+J job/hour, and we are told that it equals to 1/4 job/hour.
Thus given that T+J=1/4 job/hour.
(1) Jack is painting twice as fast as Tom --> J=2T --> T+2T=1/4 --> T=1/12 --> J=2/12=1/6 --> (time)=(reciprocal of rate)=6 hours. Sufficient.
(2) If Tom painted twice as fast as he actually does, the brothers would finish the work in 3 hours. This statement implies that if the rate of Tom were 2T instead of T, the brothers combined rate would be 1/3 job/hour, thus 2T+J=1/3. Solving T+J=1/4 and 2T+J=1/3 gives J=1/6. Sufficient.
Answer: D.
Hope it helps.
could you explain how you come to J=2/12? I think I am looking at it the wrong way, since I would come to the following calculation:
J=2T --> 1/T+1/(2T)=1/4 --> 3/2T=1/4 --> 2T=12 T=6.
I am trying to turn my calculation around but still always get the same wrong answer.