Question

There are two identical shacing machines $S_1$ and $S_2$. In machine $S_1$, the width of the workpiece is increased $10$% and the feed is decreased by $10$%, with respect to that of $S_1$. If all other conditions remain the same then the ratio of total time per pass in $S_1$ and $S_2$ will be
(round off to one decimal place).

Answer 1

$\text{Given feed for machine}1\text{is}{f}_1\text{and feed for machine 2}{f}_2$

$\text{Cutting time,}{t}_1=\frac{B_1}{f_1{N}_1}$

$\text{Cutting time,}{t}_1=\frac{B_2}{f_2{N}_2}=\frac{1.1B_1}{0.9f_1\times N_2}$

Ratio of cutting time,

$\frac{t_1}{t_2}=\frac{B_1/f_{1}N}{\frac{1.1B_1}{0.9f_{1}N}}=\frac{0.9}{1.1}=0.8$