Question

a aircraft rated at 484 hp at 2,175 rpm will produce 487 hp at what rpm? (2 decimals if needed)
question 6 2 pts
an aircraft with an engine rated at 160 hp at 2400 rpm, will produce what hp at 1,743 rpm? (2 decimals if needed)

Explanation:

Step1: Assume power - RPM relationship is linear

We assume that the horsepower (hp) and revolutions per minute (RPM) are linearly related. So, we can set up a proportion $\frac{hp_1}{RPM_1}=\frac{hp_2}{RPM_2}$.

Step2: Solve for first question

Given $hp_1 = 484$, $RPM_1=2175$, $hp_2 = 487$. We want to find $RPM_2$.
From $\frac{hp_1}{RPM_1}=\frac{hp_2}{RPM_2}$, we can cross - multiply to get $hp_1\times RPM_2=hp_2\times RPM_1$. Then $RPM_2=\frac{hp_2\times RPM_1}{hp_1}$.
Substitute the values: $RPM_2=\frac{487\times2175}{484}=\frac{1059225}{484}\approx2188.48$.

Step3: Solve for second question

Given $hp_1 = 160$, $RPM_1 = 2400$, $RPM_2=1743$. We want to find $hp_2$.
From $\frac{hp_1}{RPM_1}=\frac{hp_2}{RPM_2}$, we cross - multiply to get $hp_1\times RPM_2=hp_2\times RPM_1$. Then $hp_2=\frac{hp_1\times RPM_2}{RPM_1}$.
Substitute the values: $hp_2=\frac{160\times1743}{2400}=\frac{278880}{2400}=116.20$.

Answer:

Question 1: 2188.48
Question 2: 116.20