The distance from Xavier and David to the ranch can be found using the distance formula:
distance = sqrt((change in x)^2 + (change in y)^2 + (change in z)^2)
In this case, we are given the distances DR and XR, which represent the change in x, y, and z coordinates between the tents and the ranch. We know that the tents are located at equal distances from the ranch, so the change in x, y, and z coordinates for both David and Xavier will be the same.
Let's call the distance from each tent to the ranch "d", then we have:
DR = XR = d
Substituting the given values, we get:
12.3z + 12.4 = 10.5z + 34
Solving for z, we get:
z = 6.8
Now we can find the distance from each tent to the ranch using the formula:
distance = sqrt((change in x)^2 + (change in y)^2 + (change in z)^2)
For David's tent:
distance = sqrt((12.3z)^2 + 0^2 + (12.4)^2) = sqrt((12.3*6.8)^2 + (12.4)^2) = 87.9 meters (rounded to one decimal place)
For Xavier's tent:
distance = sqrt((10.5z)^2 + 0^2 + (34)^2) = sqrt((10.5*6.8)^2 + (34)^2) = 95.6 meters (rounded to one decimal place)
Therefore, David and Xavier are 87.9 meters and 95.6 meters away from the ranch, respectively.