OK, when we look at this problem, we're trying to figure out how much time it is for the angle to rotate around. So we need to realize we have a right triangle and we need to get some pieces of information out of it. The first thing is that in this right triangle, we can see that OQ and OD are both radii of the circle. So OQ is going to equal OP, which is going to equal 2640 miles. I want to figure out the distance of OD, however, So OD is really just OP plus PD. So PD was given as 1440 feet, but we're dealing with miles. So we're going to do a conversion one mile, 5280 feet, so 303 elevenths miles. So when I look at this ODI can see that OD is just really OP plus PD or 2640 + 3 elevenths. So we get this 29,043 / 11. Now if we look at this right triangle here, we can see that cosine Theta is just OQ divided by OD. So cosine Theta is just OQ divided by OD. Well, OQ we know is 2640 because it's a radius of the circle and OD we just found is 29,043 / 11. So when we reduce that by dividing, we get 9680 / 9681 and we take the cosine inverse of each side. So we now have an angle. We know this angle, but we actually wanted to find this arc length here. So S equal R Theta. So S equal R Theta. Remember that our Theta has to be in radians, so check your calculators and make sure you're in Radian mode and not degree. The radius we know is the same all throughout this problem. So 2640 the Theta we just found cosine inverse 968-O over 9681. So now in a full circle we know that the whole distance around is really just the circumference and the circumference is 2π R so 2π times the radius over the period, the period being 24 hours. Now that should be equal to some ratio of our arc length over the time it took to move that arc length. So our arc length with S, we found our S was 2640 cosine inverse 968 over 9681. And that's going to go that arc distance in sometime TO now to solve for T, we're just going to cross multiply and divide. And T is in hours. So because this 24 was in hours. So in order to convert it to minutes, we're just going to take this number and multiply by 60 and we'll get that 3.29. I did not do any rounding until the absolute final error final step because I didn't want to compound rounding errors.