Question

sound travels at approximately one - fifth of a mile per second. therefore, the difference in time, x (in seconds), between seeing lightning and hearing thunder can be used to estimate the distance y (in miles) between a storm and an observer. the distance of the storm can be approximated by the equation y = 0.2x where x≥0. part 1 of 2 (a) use the linear model to determine the distance between a storm and an observer for the following times between seeing lightning and hearing thunder: 3 sec, 6 sec, and 9 sec. the distance between a storm and an observer, if the time between seeing lightning and hearing thunder is 3 sec, is mi. the distance between a storm and an observer, if the time between seeing lightning and hearing thunder is 6 sec, is mi. the distance between a storm and an observer, if the time between seeing lightning and hearing thunder is 9 sec, is mi. part 2 of 2 (b) if a storm is 3.8 mi away, how many seconds will pass between seeing lightning and hearing thunder? if a storm is 3.8 mi away, seconds will pass between seeing lightning and hearing thunder.

Explanation:

Step1: Find distance for 3 seconds

Substitute $x = 3$ into $y=0.2x$.
$y = 0.2\times3=0.6$

Step2: Find distance for 6 seconds

Substitute $x = 6$ into $y = 0.2x$.
$y=0.2\times6 = 1.2$

Step3: Find distance for 9 seconds

Substitute $x = 9$ into $y=0.2x$.
$y=0.2\times9=1.8$

Step4: Find time for 3.8 miles

Given $y = 3.8$, solve for $x$ in $y = 0.2x$. So $x=\frac{y}{0.2}=\frac{3.8}{0.2}=19$

Answer:

The distance when $x = 3$ sec is $0.6$ mi.
The distance when $x = 6$ sec is $1.2$ mi.
The distance when $x = 9$ sec is $1.8$ mi.
If a storm is $3.8$ mi away, $19$ seconds will pass.