It Takes Jack 2 More Hours than Tom to Type 20 Pages GMAT Problem Solving

Question: 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?

1. 5 hours
2. 6 hours
3. 8 hours
4. 10 hours
5. 12 hours

“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”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”.
To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

Let the time needed for the Jack to type 20 pages be j hours, then for the Tom it would be j – 2 hours. So the rate of Jack is rate =\(\frac{job}{time}\) = \(\frac{20}{j}\) pages per hour and the rate of Tom rate = \(\frac{20}{j-2}\) pages per hour.

Their combined rate would be \(\frac{20}{j}\) + \(\frac{20}{j-2}\) pages per hour and this equal to \(\frac{25}{3}\) pages per hour, so: \(\frac{20}{j}+\frac{20}{j-2}=\frac{25}{3}\)

Multiply by 3: \(\frac{60}{j}+\frac{60}{j-2}={25}\)

At this point, we can either try to substitute the values from the answer choices or solve quadratic equation. Remember as we are asked to find time needed for Jack to type 40 pages, then the answer would be 2j (as j is the time needed to type 20 pages)

Answer E works:

2j = 12

j = 6

\(\frac{60}{6}+\frac{60}{6-2}\) = 10 + 15 = 25

Correct Answer: E

Approach Solution 2:

Let’s solve this question using the quadratic equations:

\(\frac{4}{t+2}+\frac{4}{t}=\frac{5}{3}\Rightarrow 0=5t^2-14t-24\Rightarrow 0=(t-4)(5t+6)\Rightarrow t=4\Rightarrow\frac{20}{6}*x=40\)

x = 12

Correct Answer: E

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