The maximum speed of a truck varies inversely with the weight of its freight. If a truck with 30,025 pounds of freight can go 55 miles per hour, what is the maximum speed of the truck with 35,250 pounds of freight? Round your answer to the nearest whole number.(1 point)

Question

The maximum speed of the truck with 35,250 pounds of freight is about
miles per hour.

Answer 1

To solve the problem, we can use the concept of inverse variation. The relationship can be expressed as:

\[ S \times W = k \]

where:

• \( S \) is the maximum speed,
• \( W \) is the weight of the freight,
• \( k \) is a constant.

From the information provided:

• For \( W = 30,025 \) pounds, \( S = 55 \) mph.

First, we calculate the constant \( k \):

\[ k = S \times W = 55 \times 30,025 \]

Calculating \( k \):

\[ k = 55 \times 30,025 = 1,648,375 \]

Next, we want to find the maximum speed \( S' \) when the weight \( W' \) is \( 35,250 \) pounds:

\[ S' \times 35,250 = 1,648,375 \]

Solving for \( S' \):

\[ S' = \frac{1,648,375}{35,250} \]

Now we calculate \( S' \):

\[ S' \approx 46.8 \]

Rounding to the nearest whole number gives us:

\[ S' \approx 47 \]

Thus, the maximum speed of the truck with 35,250 pounds of freight is about 47 miles per hour.