the flash of lightning travels at the speed of light, which is about 186,000 miles per second. The sound of lightning (thunder) travels at the speed of sound, which is about 750 miles per hour. a) if you see a flash of lightning, then hear the thunder 4 seconds later how far away is the lightning? b) Now let's generalize this result. Suppose it takes n seconds to hear the thunder after a flash of lightning. How far away is the lightning in terms of n?

The first thing we are going to do is convert 750 miles per hour to miles per second. To do that we are going to take advantage of the fact that 1 minute is 60 seconds:
[tex]( \frac{752mi}{hr} )( \frac{1hr}{60seconds})=12.53 [/tex] miles per second.

Part 1. To check how far is the flash of lightining you hear 4 seconds after seeing its light, we are going to multiply the speed of sound in miles per second by 4 seconds:
[tex](12.53 \frac{mi}{s} )(4s)=50.12mi[/tex]

We can conclude that the flash of lightening was 50.12 miles away.

Part 2. Let [tex]n[/tex] represent the seconds to hear the thunder after a flash of lightning. Since we know that the speed of sound is 12.53 miles per second, we are going to relate [tex]n[/tex] with the speed of sound using a linear function as follows:
[tex]f(n)=12.53n[/tex]
where
[tex]n[/tex] is the time in seconds 

We can conclude that the function to represent how far is a flash of lightning in terms of [tex]n[/tex] is [tex]f(n)=12.53n[/tex].