SOLUTION: Use the given information to answer the question. The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the cub

Question 1128630: Use the given information to answer the question.
The horsepower (hp) that a shaft can safely transmit varies jointly with its speed (in revolutions per minute (rpm)) and the cube of the diameter. If the shaft of a certain material 3 inches in diameter can transmit 40 hp at 110rpm, what must the diameter, d, be in order to transmit 60 hp at 150 rpm? (Round your answer to two decimal places.)
My work so far have been:
hp = k*rpm*d^3
40= k*110*27
k = 40/2970= 0.01
60= 0.01*150*d^3 = 1.5d^3
d^3 = 60/1.5
* Before my answer kept being 13.3333333. Afterwards another tutor demonstrated a way to solve the equation and his answer was 3.41 inches. However, that answer was still tagged incorrect. Is there as step missing that I'm missing? Thanks.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Let be the speed (rpm)
Let be the diameter of the shaft (inches)
Let be the horsepower transmitted
Then the first sentence of the problem is expressed in terms of , , and as:

for some constant
You are told that when and , then :

now, what diameter must the shaft have in order to safely transmit hp at rpm
You are given a value for and , and are asked the value of :
...plug in given values

(inches)

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