Algebra with math

Question

The horsepower​ (hp) that a shaft can safely transmit varies jointly with its speed​ (in revolutions per​ minute, rpm) and the cube of its diameter. If a shaft of a certain material 2 inches in diameter can transmit 36 hp at 75​ rpm, what diameter must the shaft have in order to transmit

150

hp at

20

​rpm?

Answer 1

h1/s1(d1)^3 = h2/s2(d2)^3

36/75(2)^3 = 150/20(d2)^3

36/600= 150/20(d2)^3

36(20)d2^3 = 600(150)

d2^3 = 600(150)/36(20)

d2^3 = 125

d = 5