In one year, there are 365 days. In one day, there are 24 hours.
The number of minutes in an year is,
[tex]\begin{gathered} N=365\times24\times60 \\ N=525600 \end{gathered}[/tex]The Perseid meteor appear every 1 1/5 minutes.
The number of Perseid meteors in one year is,
[tex]\begin{gathered} P=\frac{N}{1\frac{1}{5}} \\ =\frac{525600}{\frac{5\times1+1}{5}} \\ =438000 \end{gathered}[/tex]The Leonid meteor appear every 4 2/3 minutes.
The number of Leonid meteors showered in one year is,
[tex]\begin{gathered} L=\frac{N}{4\frac{2}{3}} \\ L=\frac{525600}{\frac{4\times3+2}{3}} \\ =\frac{525600\times3}{14} \end{gathered}[/tex]The number of Persoid meteors more than the Leonid meteors is,
[tex]\begin{gathered} n=N-L \\ =438000-\frac{525600\times3}{14} \\ =\frac{4555200}{14} \\ =\frac{2277600}{7} \end{gathered}[/tex]Let m be the number of times Persoid meteors is more than the Leonid meteors in each minute. Then,
[tex]\begin{gathered} m=\frac{\frac{N}{1\frac{1}{5}}}{\frac{N}{4\frac{2}{3}}} \\ =\frac{4\frac{2}{3}}{1\frac{1}{5}} \\ =\frac{\frac{4\times3+2}{3}}{\frac{5\times1+1}{5}} \\ =\frac{\frac{14}{3}}{\frac{6}{5}} \\ =\frac{70}{18} \\ =\frac{35}{9}=3\frac{8}{9} \end{gathered}[/tex]Therefore, Persoid meteors is 3 8/9 times more than the Leonid meteors showered in each minute
