Lost at Sea: The Search for Longitude

You're invited on a transatlantic cruise aboard an oceangoing yacht, the Miss Adventure, leaving from England. Soon after setting sail, you encounter storms that last for weeks. Then a devilishly thick fog envelops the ship for several days. When the fog finally lifts, the sun is at its apex, and a speck of land is faintly visible on the horizon. "Land ho!" calls the lookout. The captain determines quickly with his sextant that the ship is at latitude 42 degrees north, but then discovers to his horror that his chronometer has stopped. "Oh no!" he shouts, "Where are we?" Thinking fast, you glance at your super-accurate watch, which is set to Greenwich time. It reads 4:40 p.m. Knowing that Greenwich time is the time at the prime meridian of the world, which is 0 degrees longitude, you perform a quick mental calculation and check the map. "No problem, Cap'n," you call out confidently. "That land is...

(HINT: The Earth rotates in an easterly direction at a rate of about 15 degrees per hour, or 5 degrees every 20 minutes.)

(ANOTHER HINT: When the sun is at its apex, it's as high in the sky as it's going to be that day. That means it's noon.)