This problem is from the Treviso Arithmetic, the first primed arithmetic text, d

Question

This problem is from the Treviso Arithmetic, the first primed arithmetic text, dated 1478: The Holy Father sent a courier from Rome to Venice, commanding him that he should reach Venice in 7 days. And the most illustrious Signoria of Venice also sent another courier to Rome, who should reach Rome in 9 days. And from Rome to Venice is 250 miles. It happened that by order of these lords the couriers started their journeys at the same time. It is required to find in how many days they will meet, and how many miles each will have traveled.^37

Explanation / Answer

Let's suppose they will reach their respective destinations in given time of 7 and 9 days only.

So, their speeds are:

250/7 = 35.71 and 250/9 = 27.77 miles per day.

So, they will meet in:

250/(35.71 + 27.77) = 3.93 days

So. each would have travelled:

35.71 * 3.93 = 140.34 miles

27.77 * 3.93 = 109.13 miles

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