Question

Speeds of pulleys are inversely proportional to the length of their diameter. Diameter of pulley A is 20 cm. and diameter of pulley B is 10 cm. If B turns at 348 ​rpm, how fast does pulley A​ turn?

Answer 1

To find the speed at which pulley A turns, we use the inverse proportionality of pulley speed and diameter, which gives us a speed for pulley A of 174 rpm.

Step-by-step explanation:

Since the speeds of pulleys are inversely proportional to the length of their diameters, we can set up a proportion to find the speed of pulley A. The relationship between diameter and speed can be expressed as Speed A x Diameter A = Speed B x Diameter B. Given that the diameter of pulley A is 20 cm and the diameter of pulley B is 10 cm, and that pulley B turns at 348 rpm, we can find the speed of pulley A.

Using the proportion:

Speed A x 20 cm = 348 rpm x 10 cm,

we can solve for Speed A:

Speed A = (348 rpm x 10 cm) / 20 cm = 174 rpm.

Therefore, pulley A turns at 174 rpm.

Answer 2

174 rpm

Step-by-step explanation:

The question says that the speed is inversely proportional to the length. Thus, Inverse means, as the diameter increases, the speed reduces, or as the diameter reduces, the speed increases.

Thus, from the question, if diameter A is 20, and B is 10, then definitely, the speed will increase from 348 to a higher rate. Mathematically, we have

20 / 10 = 348 / x, where x is the missing speed.

2 = 348 / x

x = 348 / 2

x = 174 rpm

Therefore, the pulley A must have been running at a speed of 174 rpm