Question

Someone please help me with this

Your distance from lightning varies directly with the time it takes you to hear thunder. If you hear thunder 10
seconds after you see the lightning, you are about 2 miles from the lightning.

a. Write a direct variation equation for the relationship between time and distance.

b. Estimate how many seconds it would take for the thunder to travel a distance of 4 miles.
​

Answer 1

`a.\ D=(1)/(5)t`

b. 20 seconds

Explanation:

Let
`D` be the distance in miles and

`t` be the time in seconds and

`s` be the speed in miles/sec

Formula for Distance is given as:

`Distance = Speed * Time\\OR\\D=st`

Given that:

Distance = 2 miles and

Time = 10 seconds

Putting the values in formula:

`2=s* 10\\\Rightarrow s =(1)/(5) \ miles/sec`

Answer a:

Putting the value of
`s` back in the formula to find the direct variation equation for the relationship between time and distance:

`D=(1)/(5)t`

Answer b:

Using the above formula and putting
`D=4\ miles`:

`4=(1)/(5)t\\\Rightarrow t =\bold{20\ seconds}`