Question

Roger and Bill are scuba diving. Roger is at an elevation of -24 feet, and he is descending at a rate of 12 feet per minute. Bill is at an elevation of -8 feet and he is descending at a rate of 16 feet each minute. The variable t represents the time in minutes. After how many minutes will Roger and Bill be at the same elevation? At what elevation will they be at that time?

Answer 1

-7-72

Explanation:

o find when Roger and Bill will be at the same elevation, we need to set their elevation functions equal to each other and solve for the time
`(\(t\))`.

The elevation function for Roger is given by
`\(E_R(t) = -24 - 12t\)`, where
`\(t\)` is the time in minutes.

The elevation function for Bill is given by
`\(E_B(t) = -8 - 16t\)`.

Setting
`\(E_R(t) = E_B(t)\)`:


`\[-24 - 12t = -8 - 16t\]`

Now, solve for
`\(t\)`:


`\[4t = 16\]\\\[t = 4\]`

After 4 minutes, Roger and Bill will be at the same elevation.

Now, substitute
`\(t = 4\)` into either elevation function to find the elevation at that time. Let's use Roger's function:




So, after 4 minutes, Roger and Bill will be at the same elevation of -72 feet.