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16 Sep 2014, 00:39
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
44% (03:08) correct
56%
(02:53)
wrong
based on 253
sessions
History
Date
Time
Result
Not Attempted Yet
Jack takes 2 hours longer than Tom to type 20 pages. When they work together, they can type 25 pages in 3 hours. How long would it take for Jack to type 40 pages by himself?
A. 5 hours
B. 6 hours
C. 8 hours
D. 10 hours
E. 12 hours
A. 5 hours
B. 6 hours
C. 8 hours
D. 10 hours
E. 12 hours
16 Sep 2014, 00:39
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Bookmarks
Official Solution:
Jack takes 2 hours longer than Tom to type 20 pages. When they work together, they can type 25 pages in 3 hours. How long would it take for Jack to type 40 pages by himself?
A. 5 hours
B. 6 hours
C. 8 hours
D. 10 hours
E. 12 hours
Let \(j\) hours represent the time needed for Jack to type 20 pages. For Tom, it would take \(j-2\) hours to type the same 20 pages. Therefore, Jack's rate is given by \(rate = \frac{job}{time}=\frac{20}{j}\) pages per hour, and Tom's rate is \(rate=\frac{job}{time}=\frac{20}{j-2}\) pages per hour.
Their combined rate is the sum of their individual rates, which is \(\frac{20}{j}+\frac{20}{j-2}\) pages per hour. This combined rate is equal to \(\frac{25}{3}\) pages per hour, so we have: \(\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}\). Multiplying through by 3, we get: \(\frac{60}{j}+\frac{60}{j-2}=25\). At this point, we can either substitute the values from the answer choices or solve the quadratic equation. Since we are asked to find the time needed for Jack to type 40 pages, the answer would be \(2j\) (because \(j\) is the time needed to type 20 pages).
Answer E works:
\(2j=12\);
\(j=6\);
Substituting \(j\) into the equation: \(\frac{60}{6}+\frac{60}{6-2}=10+15=25\).
Answer: E
Jack takes 2 hours longer than Tom to type 20 pages. When they work together, they can type 25 pages in 3 hours. How long would it take for Jack to type 40 pages by himself?
A. 5 hours
B. 6 hours
C. 8 hours
D. 10 hours
E. 12 hours
Let \(j\) hours represent the time needed for Jack to type 20 pages. For Tom, it would take \(j-2\) hours to type the same 20 pages. Therefore, Jack's rate is given by \(rate = \frac{job}{time}=\frac{20}{j}\) pages per hour, and Tom's rate is \(rate=\frac{job}{time}=\frac{20}{j-2}\) pages per hour.
Their combined rate is the sum of their individual rates, which is \(\frac{20}{j}+\frac{20}{j-2}\) pages per hour. This combined rate is equal to \(\frac{25}{3}\) pages per hour, so we have: \(\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}\). Multiplying through by 3, we get: \(\frac{60}{j}+\frac{60}{j-2}=25\). At this point, we can either substitute the values from the answer choices or solve the quadratic equation. Since we are asked to find the time needed for Jack to type 40 pages, the answer would be \(2j\) (because \(j\) is the time needed to type 20 pages).
Answer E works:
\(2j=12\);
\(j=6\);
Substituting \(j\) into the equation: \(\frac{60}{6}+\frac{60}{6-2}=10+15=25\).
Answer: E
General Discussion
03 Oct 2014, 20:57
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Hi Bunuel I solved this problem a different way, but the result is different plz correct me why I am wrong !
Jack: x ( page/hr)
Tom: y ( page/hr)
we have : x + y = 25/3 (page/hr); (1/x - 1/y) = (2/20)
solving these two equations I have 2 values of x, which are x1 = 25 (p/hr) and x2 = 10/3 (p/hr)
so I cannot figure out the expected result !!!!
tks Bunuel
Jack: x ( page/hr)
Tom: y ( page/hr)
we have : x + y = 25/3 (page/hr); (1/x - 1/y) = (2/20)
solving these two equations I have 2 values of x, which are x1 = 25 (p/hr) and x2 = 10/3 (p/hr)
so I cannot figure out the expected result !!!!
tks Bunuel
