Problem 9.2. In the first hour of the shift, the master made 35 parts. Then he realized that, maintaining the current speed, he would have to stay an extra hour to complete the shift's plan. By increasing his speed by 15 parts per hour, he completed the plan half an hour before the end of the shift. How many parts should the master produce during the shift?
Answer: 210.

Solution. Let $N$ be the number of parts he still needs to manufacture. If he continued to make 35 parts per hour, he would finish in $\frac{N}{35}$ hours. When he sped up and started producing 50 parts per hour, he completed the work in $\frac{N}{50}$ hours.

From the condition, it follows that $\frac{N}{35}-\frac{N}{50}=1.5$, which means $\frac{3}{350} N=1.5$, from which we find $N=175$. Then the number of parts that need to be manufactured in one shift is $175+35=210$.