【Explanation】: To find the linear speed of the truck, we need to calculate the distance that a point on the circumference of the wheel travels in a given amount of time. The linear speed is the product of the circumference of the wheel and the number of revolutions per minute. The circumference of a circle is given by the formula \( C = 2\pi r \), where \( r \) is the radius of the circle.
First, we'll calculate the circumference of the wheel:
Given the radius \( r = 18 \) inches, the circumference \( C \) is:
\[ C = 2\pi r = 2\pi \times 18 \]
Next, we'll convert the revolutions per minute (rpm) to revolutions per hour (rph) to match the units with miles per hour:
\[ 274 \text{ rpm} \times 60 \text{ minutes per hour} = 16440 \text{ rph} \]
Now, we'll calculate the distance traveled in one hour by multiplying the circumference by the number of revolutions per hour:
\[ \text{Distance per hour} = C \times \text{rph} \]
\[ \text{Distance per hour} = 2\pi \times 18 \times 16440 \]
Since the circumference is in inches, we'll convert the distance to miles. There are 63360 inches in a mile (5280 feet per mile times 12 inches per foot):
\[ \text{Distance per hour in miles} = \frac{2\pi \times 18 \times 16440}{63360} \]
Now, let's calculate the values step by step:
1. Calculate the circumference:
\[ C = 2\pi \times 18 \]
\[ C = 36\pi \text{ inches} \]
2. Convert rpm to rph:
\[ 274 \text{ rpm} \times 60 = 16440 \text{ rph} \]
3. Calculate the distance per hour in inches:
\[ \text{Distance per hour} = 36\pi \times 16440 \]
\[ \text{Distance per hour} = 36 \times \pi \times 16440 \]
4. Convert the distance per hour to miles:
\[ \text{Distance per hour in miles} = \frac{36 \times \pi \times 16440}{63360} \]
Now, let's perform the calculations:
\[ \text{Distance per hour in miles} = \frac{36 \times \pi \times 16440}{63360} \]
\[ \text{Distance per hour in miles} = \frac{36 \times 3.14159 \times 16440}{63360} \]
\[ \text{Distance per hour in miles} = \frac{36 \times 3.14159 \times 16440}{63360} \]
\[ \text{Distance per hour in miles} = \frac{1843776}{63360} \]
\[ \text{Distance per hour in miles} \approx 29.1 \]
【Answer】: The linear speed of the truck is approximately 29.1 miles per hour.
