Let's call the aircraft carrier's average speed "x".
In the 8 hours that the aircraft carrier traveled before the submarine left, it covered a distance of 8x miles (since distance = rate x time).
When the submarine left, it started "catching up" to the aircraft carrier, which means that the distance between them was decreasing. We can set up an equation to represent this:
8x + 5(x-26) = 8x + 5x - 130
The left side of the equation represents the total distance that the submarine traveled (5 hours at a speed of x-26) plus the distance that the aircraft carrier traveled in those same 5 hours (since they met up after 5 hours). The right side of the equation represents the total distance that the aircraft carrier traveled in those 5 hours (since it traveled at a constant speed of x).
Simplifying the equation:
13x - 130 = 16x
Subtracting 13x from both sides:
-130 = 3x
Dividing both sides by 3:
x = -43.33
Wait a minute... a negative speed? That doesn't make sense.
The issue here is that we made an incorrect assumption: we assumed that the aircraft carrier and submarine were traveling in the same direction. However, the problem doesn't actually specify which direction the aircraft carrier was traveling in.
Let's try this again, but this time we'll assume that the aircraft carrier was traveling west (since that's the only other direction it could be traveling in).
In 8 hours, the aircraft carrier would have traveled 8x miles to the west.
When the submarine left, it started "catching up" to the aircraft carrier by traveling to the west as well. We can set up an equation to represent this:
8x - 5(x+26) = 8x - 5x - 130
The left side of the equation represents the total distance that the submarine traveled (5 hours at a speed of x+26) minus the distance that the aircraft carrier traveled in those same 5 hours (since they met up after 5 hours). The right side of the equation represents the total distance that the aircraft carrier traveled in those 5 hours (since it traveled at a constant speed of x to the west).
Simplifying the equation:
3x - 130 = 3x
Subtracting 3x from both sides:
-130 = 0
Uh oh, we ended up with an equation that doesn't make sense.
The issue here is that we made another incorrect assumption: we assumed that the submarine caught up to the aircraft carrier exactly 5 hours after it left. However, we don't actually know how long it took the submarine to catch up.
Let's call the amount of time it took the submarine to catch up "t".
In the 8 hours that the aircraft carrier traveled before the submarine left, it covered a distance of 8x miles.
When the submarine left, it started "catching up" to the aircraft carrier by traveling to the west. We can set up an equation to represent this:
8x - t(x+26) = 8x - xt
The left side of the equation represents the total distance that the submarine traveled (t hours at a speed of x+26) minus the distance that the aircraft carrier traveled in those same t hours (since they met up after t hours). The right side of the equation represents the total distance that the aircraft carrier traveled in those t hours (since it traveled at a constant speed of x to the west).
Simplifying the equation:
8x - t(x+26) = 8x - xt
8x - tx - 26t = 8x - xt
8x - 8x - tx + xt - 26t = 0
-x(t-26) - 26t = 0
-x(t-26) = 26t
-x = 26
x = -26
Uh oh, another negative speed.
The issue here is that we made yet another incorrect assumption: we assumed that the aircraft carrier and submarine were traveling in a straight line. However, in reality they would have been traveling along the surface of the Earth, which is curved. This means that their paths would have intersected at some point, which would have affected the distance that the submarine traveled.
So unfortunately, we can't actually solve this problem with the information given. We would need to know more about the paths that the aircraft carrier and submarine took in order to determine the aircraft carrier's average speed.