The Family of Elkanah

Now there was a certain man of Ramathaim Zophim, of the mountains of Ephraim, and his name was Elkanah the son of Jeroham, the son of Elihu, the son of Tohu, the son of Zuph, an Ephraimite. And he had two wives: the name of one was Hannah, and the name of the other Peninnah. Peninnah had children, but Hannah had no children. This man went up from his city yearly to worship and sacrifice to the Lord of hosts in Shiloh. Also the two sons of Eli, Hophni and Phinehas, the priests of the Lord, were there. And whenever the time came for Elkanah to make an offering, he would give portions to Peninnah his wife and to all her sons and daughters. But to Hannah he would give a double portion, for he loved Hannah, although the Lord had closed her womb. And her rival also provoked her severely, to make her miserable, because the Lord had closed her womb. So it was, year by year, when she went up to the house of the Lord, that she provoked her; therefore she wept and did not eat.

Then Elkanah her husband said to her, “Hannah, why do you weep? Why do you not eat? And why is your heart grieved? Am I not better to you than ten sons?”

A. In a cylindrical womb with radius 1/2m, the sons are rising at a rate of 3 sons/s. What is the rate of increase of the value of husbands?

B. Given Peninnah = 6 and Hson/Hdaughter = 0, find P/PH (r2h).

C. Hannah has not eaten in three days. The rate of husband-value over son-value increases every four days. How many days will it take Hannah to eat Elkanah?

D. Hannah is standing on the edge of the Jordan river. She has ten sons. Her husband Elkanah is on the other side of the river and weighs ≥ ten sons. The boat can bear the weight of four sons, or a wifely double portion. Elkanah cannot ride in the same boat as Hannah’s sons. How many trips will it take her to reach Shiloh?

E. Is Elkanah better than ten sons? Show your work.