Math CentralQuandaries & Queries


Question from manish, a student:

train fares are proportional to the sq .root of distance traveled. the train fare is Rs. 24.4 for a distance of 140 kms. by how much % does the total fare increase if the same distance is covered by breaking the journey after every 35 kms.

Hi Manish,

Suppose the fare in Rs. is $F$ and the distance traveled in kms is $d.$ The fact that the train fares are proportional to the square root of distance traveled means that there is a constant $k$ so that

\[F = k \times \sqrt{d}.\]

You know $F$ and $d$ for one trip so use that information to find $k.$ Use this value of $k$ to determine the fare for a 35 km trip. How many of these will you need to travel 140 km?


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