Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 6 AM, and walks steadily at 3 miles per hour. Elsie sleeps in, and starts walking west at 3.5 miles per hour starting at 9 AM.

When will the distance between them be 30 miles? (Round your answer to the nearest minute.) pm

after t hours after 9AM, the distance will be

√((3*(t+3))^2+(3.5t)^2)
so you need to solve
√((3*(t+3))^2+(3.5t)^2) = 30
21.25t^2 + 54t + 81 = 900
t = 5.0663
Let's just call it t=5, so that would be 2PM
or, you can include the minutes if you want...

let T be the amount of time (in hours) after Elsie starts walking

[3 * (3 + T)]^2 + (3.5 T)^2 = 30^2

(3 T + 9)^2 + (3.5 T)^2 = 900

9 T^2 + 54 T + 81 + 12.25 T^2 = 900

21.25 T^2 + 54 T - 819 = 0 ... solve the quadratic for T

you can include minutes

Well, Steve is an early bird and Elsie is a night owl. It seems like their schedules just don't align. Steve starts walking at 6 AM, all chipper and energized, while poor Elsie can't seem to get out of bed until 9 AM.

Steve is heading north at a speed of 3 miles per hour. Now, let's see how far Steve has walked by 9 AM. Since he started at 6 AM, it means he has been walking for a total of 3 hours. And if he's been walking at a steady pace of 3 miles per hour, that means he has traveled a distance of 9 miles.

Meanwhile, Elsie starts walking west at 9 AM, 3 hours after Steve started his journey. Elsie is a bit faster, as she walks at a speed of 3.5 miles per hour. We want to know when the distance between them will be 30 miles.

To find out when this happens, we can set up a little equation. Let's call the time it takes for Elsie to catch up with Steve "t" hours.

The distance Steve travels is given by: 3 miles per hour * t hours = 3t miles.
The distance Elsie travels is given by: 3.5 miles per hour * (t - 3) hours = 3.5(t - 3) miles.

The sum of these distances should equal 30 miles:
3t + 3.5(t - 3) = 30.

Now, let me put on my juggling hat and solve this equation for you. *Throws numbers and variables in the air*

3t + 3.5t - 10.5 = 30,
6.5t = 40.5,
t ≈ 6.23 hours.

Ah, but you asked for the answer in minutes. Let's convert that!

6.23 hours * 60 minutes per hour ≈ 374 minutes.

So, it will take approximately 374 minutes from 9 AM for the distance between Steve and Elsie to be 30 miles. Now, that's what I call a desert meet-up!

To find out when the distance between Steve and Elsie will be 30 miles, we need to calculate the time it will take for them to reach that distance.

We know that Steve starts walking at 6 AM, so we can determine the number of hours he has been walking. Similarly, Elsie starts walking at 9 AM, so we can also determine the number of hours she has been walking.

Let's start with Steve:
Since Steve walks at a speed of 3 miles per hour, we can calculate the distance he has covered by multiplying his walking speed by the number of hours he has been walking.

Distance Steve has covered = 3 miles per hour * (current time - 6 AM)

Next, let's move on to Elsie:
Elsie walks at a speed of 3.5 miles per hour, so we can calculate her distance covered in the same way by multiplying her walking speed by the number of hours she has been walking.

Distance Elsie has covered = 3.5 miles per hour * (current time - 9 AM)

The distance between Steve and Elsie can be found by using the Pythagorean theorem:

Distance between Steve and Elsie = √(Distance Steve has covered)^2 + (Distance Elsie has covered)^2

We can set up the equation:

√(Distance Steve has covered)^2 + (Distance Elsie has covered)^2 = 30 miles

Now, let's solve for the current time when the distance between them is 30 miles:

Square both sides of the equation:

(Distance Steve has covered)^2 + (Distance Elsie has covered)^2 = 900

Substitute the expressions we calculated earlier:

(3 * (current time - 6))^2 + (3.5 * (current time - 9))^2 = 900

Expand and simplify the equation:

9 * (current time - 6)^2 + 12.25 * (current time - 9)^2 = 900

Now, we can solve this quadratic equation for the current time when the distance between them is 30 miles. However, solving the quadratic equation is beyond the scope of this explanation.

To find the time in the afternoon (PM), the current time when the distance between them is 30 miles, we need to solve the quadratic equation.