3.4: Hidden connections

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Problem 88 Two old women set out at sunrise and each walked with a constant speed. One went from A to B, and the other went from B to A. They met at noon, and continuing without a stop, they arrived respectively at B at 4 pm and at A at 9 pm. At what time was sunrise on that day?

Problem 89 A paddle-steamer takes five days to travel from St Louis to New Orleans, and takes seven days for the return journey. Assuming that the rate of flow of the current is constant, calculate how long it takes for a raft to drift from St Louis to New Orleans.

Problem 90 [From Paolo dell’Abbaco’s Trattato d’aritmetica] “From here to Florence is 60 miles, and there is one who walks it in 8 days [in one direction], another in five days [in the opposite direction]. It is asked: Departing at the same time, in how many days will they meet?”

Problem 91 Notice that in Problem 88 sunrise occurs $t = \sqrt{4 \times 9}$ hours before noon, and that $\sqrt{4 \times 9}$ is the geometric mean of 4 and 9. Once this is pointed out, can you reformulate your solution to Problem 88 to solve a more general problem?

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