To find the relationship between \( d \) and \( v \), we can assume a linear relationship based on the given points. The problem states that \( d \) is partly constant and partly varies with \( v \).
Let’s define the relationship as follows:
\[ d = k + mv \]
Where:
- \( k \) is a constant term,
- \( m \) is the rate of change of \( d \) with respect to \( v \).
We can use the two points given:
- When \( v = 40 \), \( d = 150 \).
- When \( v = 54 \), \( d = 192 \).
This gives us the following system of equations:
- \( 150 = k + 40m \) (Equation 1)
- \( 192 = k + 54m \) (Equation 2)
Now, we can subtract Equation 1 from Equation 2 to eliminate \( k \):
\[ 192 - 150 = (k + 54m) - (k + 40m) \] \[ 42 = 14m \] \[ m = \frac{42}{14} = 3 \]
Now that we have \( m \), we can substitute it back into one of the equations to find \( k \). Using Equation 1:
\[ 150 = k + 40 \cdot 3 \] \[ 150 = k + 120 \] \[ k = 150 - 120 = 30 \]
Now we have both \( k \) and \( m \):
- \( k = 30 \)
- \( m = 3 \)
So the formula connecting \( d \) and \( v \) is:
\[ d = 30 + 3v \]
Now, to find \( d \) when \( v = 73 \):
\[ d = 30 + 3 \cdot 73 \] \[ d = 30 + 219 \] \[ d = 249 \]
Therefore, when \( v = 73 \), \( d = 249 \).