From the Treviso Arithmetic, the first printed arithmetic text, dated 1478: The

Question

From the Treviso Arithmetic, the first printed 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.

Explanation / Answer

distance between cities = 250 miles rome to venice courier be RV and venice to rome courier be VR RV travels 250 miles in 7 days, so speed = 250/7 miles/day and VR travels 250 miles in 9 days, so speed of VR = 250/9 miles/day let they meet after x days distance traveled by RV = x*250/7 miles distance traveled by VR = x*250/9 miles sum should be equal to 250 miles. so x*250[(1/7)+(1/9)] = 250 so x = 63/15 = 4.2 days so they meet on 5th day distance traveled by Rome to venice courier = x*250/7 = 150 miles distance traveled by venice to rome courier = x*250/9 = 100 miles

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