Quote:
It takes Jack 2 more hours than Tom to type 20 pages. If working together, Jack and Tom can type 25 pages in 3 hours, how long will it take Jack to type 40 pages?
A. 5 hours
B. 6 hours
C. 8 hours
D. 10 hours
E. 12 hours
I received a PM about this problem.
Since Jack and Tom together can type 25 pages in 3 hours, their combined rate = \(\frac{work}{time}\) = \(\frac{25}{3}\) = 8\(\frac{1}{3}\) pages per hour.
We can PLUG IN THE ANSWERS, which represent Tom's time to type 40 pages.
When the correct answer choice is plugged in, the combined rate for Jack and Tom will be 8\(\frac{1}{3}\) pages per hour.
D: 10 hoursHere, Jack takes 10 hours to type 40 pages, implying that Jack's time to type 20 pages = 5 hours.
Thus, Jack's rate = \(\frac{work}{time}\) = \(\frac{20}{5}\) = 4 pages per hour.
Since Jack takes 2 more hours than Tom to type 20 pages, Tom's time to type 20 pages = 5-2 = 3 hours.
Thus, Tom's rate = \(\frac{work}{time}\) = \(\frac{20}{3}\) = 6\(\frac{2}{3}\) pages per hour.
Combined rate for Jack and Tom = 4 + 6\(\frac{2}{3}\) = 10\(\frac{2}{3}\) pages per hour.
Their combined rate is TOO FAST.
To decrease their combined rate, Jack must take MORE TIME to type 40 pages.
The correct answer is:
.
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