Answer
(a) 30 degree Fahrenheit
(b) 22.5 degree Fahrenheit
Work Step by Step
(a) From the table, to find the wind chill index (WCI), we match the wind speed(v) with the corresponding temperature(T).
$WCI = 16^oF, v = 25mi/h$
Hence from the table the temperature that correspond with the wind speed to give the value of the wind chill index is $T = 30^oF$
(b) The wind chill index (WCI) at wind speed of $25mi/h$ will $3^oF$ and $9^oF$ with the corresponding temperature of $20^oF$ and $25^oF$ respectively
We need to find the value by which the temperature increases from $20^oF$ at the WCI of $6^oF$
In order to do so we are going to break down the $WCI = 6^oF$ into two values, the first part should be an already existing WCI in the table that is less than the 6 at $v = 6mi/h$
$WCI = 6^F = 3^oF + 3^oF$ (Equation 1)
From here we find the difference between the WCI of 3 and 9 and we multiply that by a fractional value to make it equal to the second value of (Equation 1). After that we substitute it into the (Equation 1).
$WCI = 3 + \frac{1}{2}(9-3)$ (Equation 2)
The fraction we seek is the coefficient of the Difference in the WCI's in (Equation 2) which is $\frac{1}{2}$
Now using that fraction, we can find our temperature increase and subsequently our estimated Temperature
$Temperature Increase = \frac{1}{2}(25 - 20)$
$Estimated Temperature (T) = 20 + Temperature Increase$
$T = 20 + \frac{1}{2}(25 - 20) = 22.5^oF$
Therefore when $WCI = 6^oF$ and $v = 25mi/h$, the temperature becomes $22.5^oF$
