Question

In the last several weeks, 22 days saw rain and 97 days saw high winds. In that same time period, 13 days saw both rains and high winds. How many days saw either rain or high winds?

Answer 1

Given:

The number of rain days is n(r) = 22 days.

The number of high wind days is n(w) = 97 days.

The number of days with both rains and high winds is n(b) = 13 days.

The objective is to find the number of days either rain or high winds.

Explanation:

The number of days with only rain can be calculated as,

$\begin{gathered} n(R)=n(r)-n(b) \\ =22-13 \\ =9\text{ days} \end{gathered}$

Similarly, the number of days with only high wind can be calculated as,

$\begin{gathered} n(W)=n(w)-n(b) \\ =97-13 \\ =84\text{ days} \end{gathered}$

To find either rain or high winds:

The number of days with either rain or high winds can be calculated as,

$n(R\text{ or W)=n(R)+n(W)}$

On plugging the obtained values in the above equation,

$n(R\text{ or W)}=9+84=93\text{days}$

Hence, the number of days either rain or high winds is 93 days.