Calculate the values of x and y in the following table? $$\begin{array} { | l | l | l | l | }
\hline \multicolumn{2}{|l|} { \text { Pulley A } } & \text { Pulley B } \
\hline \text { Diameter } & \mathrm { rpm } & \text { Diameter } & \mathrm { rpm } \
\hline 34 \mathrm {~cm} & 54 & 68 \mathrm {~cm} & x \
\hline 18 \mathrm {~cm} & y & 12 \mathrm {~cm} & 96 \
\hline
\end{array}$$
A) x = 108, y = 32
B) x = 27, y = 64
C) x = 13.5, y = 64
D) x = 108, y = 64
E) x = 13.5, y = 32

Question

Calculate the values of x and y in the following table? $$\begin{array} { | l | l | l | l | } 
\hline \multicolumn{2}{|l|} { \text { Pulley A } } & \text { Pulley B } \
\hline \text { Diameter } & \mathrm { rpm } & \text { Diameter } & \mathrm { rpm } \
\hline 34 \mathrm {~cm} & 54 & 68 \mathrm {~cm} & x \
\hline 18 \mathrm {~cm} & y & 12 \mathrm {~cm} & 96 \
\hline
\end{array}$$
A) x = 108, y = 32
B) x = 27, y = 64
C) x = 13.5, y = 64
D) x = 108, y = 64
E) x = 13.5, y = 32

Quizplus · Accepted Answer

The relationship between the diameters and rpm of pulleys in a belt drive system is given by the formula $D_1 \times N_1 = D_2 \times N_2$, where $D_1$ and $D_2$ are the diameters of the pulleys, and $N_1$ and $N_2$ are their respective rpms. For Pulley A and Pulley B with diameters 34 cm and 68 cm, respectively, and given that Pulley A has an rpm of 54, we can find $x$ by setting up the equation $34 \times 54 = 68 \times x$, which simplifies to $x = 27$. For the second set of pulleys with diameters 18 cm and 12 cm, and given that Pulley B has an rpm of 96, we can find $y$ by setting up the equation $18 \times y = 12 \times 96$, which simplifies to $y = 64$.

Calculate the Values of X and Y in the Following