The horsepower produced by the steam engine varies directly as the number of revolution per minute of its operation. If 800 horsepower was produced when a machine was operated at 175 revolutions per minute. Find the horsepower it will produce when it operates at 190 revolutions per minute?
x/190 = 800/175
600 150 operates at 200 revolution per minute
To solve this problem, we need to use the concept of direct variation. Direct variation means that two quantities are related in such a way that when one increases, the other also increases by the same factor.
In this case, the horsepower produced is directly proportional to the number of revolutions per minute. We can write this relationship as:
Horsepower ∝ Number of revolutions per minute
To find the specific equation that relates horsepower and revolutions per minute, we need to determine the constant of variation. We can do this using the given information that when the machine operates at 175 revolutions per minute, it produces 800 horsepower.
We can set up a proportion to find the constant of variation (k):
Horsepower₁ / Revolutions per minute₁ = Horsepower₂ / Revolutions per minute₂
800 / 175 = Horsepower₂ / 190
Simplifying this proportion, we get:
800 * 190 = 175 * Horsepower₂
152,000 = 175 * Horsepower₂
To find the value of Horsepower₂, divide both sides of the equation by 175:
Horsepower₂ = 152,000 / 175
Horsepower₂ ≈ 868.57
Therefore, when the machine operates at 190 revolutions per minute, it will produce approximately 868.57 horsepower.