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27 Feb 2019, 04:47
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Let us say Tom's time = t hours
So, Jack's time = t + 2 hours ----- (I)
Work (1) = 20 pages
Therefore Tom's rate = \(\frac{20}{t}\)
Jack's rate = \(\frac{20}{(t+2)}\) -------- (II)
Now, Work (2) = 25 pages
Time = 3 hours
Work done by Tom + Work done by Jack = Total Work
\(\frac{20}{t}\) * 3 + \(\frac{20}{(t+2)}\) * 3 = 25
Solving this becomes ,
\(25t^2 - 70t - 120t = 0\)
Divide by 5 ; \(5t^2 - 14t - 24 = 0\)
\(5t^2 - 20t + 6t - 24 = 0\)
\(5t (t - 4) + 6 (t - 4) = 0\)
t = 4 or t = -6/5 , Reject negative solution
Jack's rate =\(\frac{20}{(t + 2)}\) = \(\frac{20}{6}\) as per equation (II) above
New Work (3) = 40 pages
Time required for Jack to complete the work = \(\frac{(40*6)}{20}\)
Answer = 12 hours (E)
18 Jul 2020, 21:13
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Answer: Option E
Attachments
Screenshot 2020-07-19 at 9.41.38 AM.png [ 921.03 KiB | Viewed 2311 times ]
26 Dec 2022, 17:52
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I received a DM about this problem.
Since Jack and Tom together take 25 pages to type 3 pages, their combined rate \(= \frac{work}{time} = \frac{25}{3}\) pages per hour
We can PLUG IN THE ANSWERS, which represent the time for Jack to type 40 pages.
When the correct answer is plugged in, the combined rate for Jack and Tom \(= \frac{25}{3}\) pages per hour
B: 6 hours for Jack to type 40 pages, implying a time of 3 hours for Jack to type 20 pages and a time of 1 hour for Tom to type 20 pages (since Jack takes 2 more hours than Tom)
Jack's rate \(= \frac{work}{time} = \frac{20}{3}\) pages per hour
Tom's rate \(= \frac{work}{time} =\frac{ 20}{1} = 20\) pages per hour
Combined rate for Jack and Tom \(= \frac{20}{3} + 20 = \frac{80}{3}\) pages per hour
The combined rate is too high.
Eliminate B.
D: 10 hours for Jack to type 40 pages, implying a time of 5 hours for Jack to type 20 pages and a time of 3 hours for Tom to type 20 pages (since Jack takes 2 more hours than Tom)
Jack's rate \(= \frac{work}{time }= \frac{20}{5} = 4\) pages per hour
Tom's rate \(= \frac{work}{time} = \frac{20}{3}\) pages per hour
Combined rate for Jack and Tom \(= 4 + \frac{20}{3} = \frac{32}{3}\) pages per hour
The combined rate is lower but still too high.
As Jack's time for 40 pages iINCREASES (from 6 to 10), the combined rate for Jack and Tom DECREASES (from 80/3 to 32/3).
Implication:
For the combined rate to decrease further to 25/3, the correct time for Jack must be greater than option D.
E: 12 hours for Jack to type 40 pages, implying a time of 6 hours for Jack to type 20 pages and a time of 4 hours for Tom to type 20 pages (since Jack takes 2 more hours than Tom)
Jack's rate \(= \frac{work}{time} = \frac{20}{6} = \frac{10}{3} \)pages per hour
Tom's rate \(= \frac{work}{time} = \frac{20}{4} = 5\) pages per hour
Combined rate for Jack and Tom \(= \frac{10}{3} + 5 = \frac{25}{3}\) pages per hour
Success!
