Question

in one year, the Perseid meteor shower had a meteor appear every o appear every 15 minutes on average. That same year, the Leonid meteor shower had a meteor appear ry 4 minutes on average

Answer 1

In one year, there are 365 days. In one day, there are 24 hours.

The number of minutes in an year is,

`\begin{gathered} N=365*24*60 \\ N=525600 \end{gathered}`

The Perseid meteor appear every 1 1/5 minutes.

The number of Perseid meteors in one year is,

`\begin{gathered} P=(N)/(1(1)/(5)) \\ =(525600)/((5*1+1)/(5)) \\ =438000 \end{gathered}`

The Leonid meteor appear every 4 2/3 minutes.

The number of Leonid meteors showered in one year is,

`\begin{gathered} L=(N)/(4(2)/(3)) \\ L=(525600)/((4*3+2)/(3)) \\ =(525600*3)/(14) \end{gathered}`

The number of Persoid meteors more than the Leonid meteors is,

`\begin{gathered} n=N-L \\ =438000-(525600*3)/(14) \\ =(4555200)/(14) \\ =(2277600)/(7) \end{gathered}`

Let m be the number of times Persoid meteors is more than the Leonid meteors in each minute. Then,

`\begin{gathered} m=((N)/(1(1)/(5)))/((N)/(4(2)/(3))) \\ =(4(2)/(3))/(1(1)/(5)) \\ =((4*3+2)/(3))/((5*1+1)/(5)) \\ =((14)/(3))/((6)/(5)) \\ =(70)/(18) \\ =(35)/(9)=3(8)/(9) \end{gathered}`

Therefore, Persoid meteors is 3 8/9 times more than the Leonid meteors showered in each minute