Two Typists Pages Written

The two typists wrote a total of 65 pages;
although the first typed for an hour longer than the second, but typed 5 pages less;
the second types 2 more pages per hour than the first.
How many pages per hour does each typist write?

Final Answer:

a =  5
b =  7

Step-by-step explanation:

$$\begin{gathered} a\cdot (t+1)+b\cdot t=65 \\ a\cdot (t+1)+5=b\cdot t \\ b=a+2 \\ {a}_1=-12 \\ {b}_1=-10 \\ {t}_1=-7/2 \\ a>0 \\ b>0 \\ t>0 \\ a=5 \\ b=7 \\ t=5 \end{gathered}$$

$b=7$

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