Raj and Vikram's Travels

Algebra Level 2

Raj and Vikram are two travelers in ancient India, walking along the Silk road. On the first day of travel, Raj travels \(5\) yojanas, and on each successive day travels \(3\) yojanas more than the previous day. Vikram started at the same place and travels the same path, but started \(5\) days earlier, and travels \(7\) yojanas a day. On which day of Raj's travel will the two of them meet?

Details and assumptions

A yojana is an ancient Indian unit of measure.

The silk road does not cross itself. Rai and Vikram will meet only if they have travelled the same distance.

If they meet at any point on the 123rd day (say at 12:34pm), then your answer is that they meet on the 123rd day.


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