Question

a persons distance from lightning varies directly with the time it takes to hear thunder. if a person hears thunder 10 seconds after seeing the lightning, they are 2 miles from the lightning. how many seconds would it take for the thunder to travel a distance of 4 miles? a 40 b $\frac{4}{5}$ c $\frac{1}{5}$ d

Explanation:

Step1: Find the speed of sound

Since distance $d$ varies directly with time $t$, and when $t = 10$ seconds, $d = 2$ miles. The speed $v$ of sound is $v=\frac{d}{t}=\frac{2}{10}=\frac{1}{5}$ miles per second.

Step2: Calculate the time for 4 - mile distance

We know $v=\frac{1}{5}$ miles per second and $d = 4$ miles. Using the formula $t=\frac{d}{v}$, we substitute the values: $t=\frac{4}{\frac{1}{5}}=4\times5 = 20$ seconds. But we made a wrong - start above. Let's use the direct - variation formula $d=kt$. When $d = 2$ miles and $t = 10$ seconds, $2 = k\times10$, so $k=\frac{2}{10}=\frac{1}{5}$. The equation is $d=\frac{1}{5}t$. When $d = 4$ miles, we solve for $t$: $4=\frac{1}{5}t$, then $t = 20$ seconds.

Answer:

20 (It seems there is a mistake in the provided options as the correct answer is 20 and it's not among A, B, C, D)