Working together, John and Jack can type 20 pages in one hou

Let the rate of John be \(x\) pages per hour and the rate of Jack \(y\) pages per hour. Then as we can sum the rates and \(rate*time=job\): \((x+y)*1=20\) --> \(x+y=20\);

"They would be able to type 22 pages in one hour if Jack increases his typing speed by 25%": \((x+1.25y)*1=22\) --> \(x+1.25y=22\);

Question: \(\frac{y}{x}=?\)

Subtract (1) from (2) --> \(x+1.25y-(x+y)=22-20\) --> \(0.25y=2\) --> \(y=8\) --> \(x=12\) --> \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\).

Answer: D.

OR: as by increasing the rate of Jack by 25% 2 more pages can be typed in one hour than we can directly write: \(0.25y=2\) --> --> \(y=8\) --> \(x=12\) --> \(\frac{y}{x}=\frac{8}{12}=\frac{2}{3}\).

Answer: D.