For heat transfer purposes, an egg can be considered to be a 5.5-cm-diameter sphere having the properties of water. An egg that is initially at 8°C is dropped into the boiling water at 100°C. The heat transfer coefficient at the surface of the egg is estimated to be 800 W/m²·K. If the egg is considered cooked when its center temperature reaches 60°C, determine how long the egg should be kept in the boiling water. Solve this problem using analytical one-term approximation method (not the Heisler charts).