   # How wide is the river?

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Pawan and Ashwin are on the two opposite banks of a river. They both have a rowing boat.

They both start at the same time towards the opposite bank. They pass each other at 180 meters from the bank where Pawan departed. When reaching the opposite bank, they both take a rest for the same amount of time before they return. On the way back, they pass each other at 100 meters from the bank from where Pawan returned.
Pawan and Ashwin both row with a constant speed, but Ashwin rows faster.

How wide is the river? posted May 6, 2014

Let X be the distance.
Since Speed = Distance/Time. From first we can conclude that:
Sa = X-180/T, Sb=180/T
=> Sa=(X-180/180)*Sb (cancelling T from the equation)

Similarly from second run if we can conclude:
Sa=2X-100/T, Sb=X+100/T
=> Sa=2X-100/X+100 (cancelling T again)

Equating both Sa and simplifying the equation we get X = 240.

Bank is 240 meters wide. answer May 7, 2014

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Can you determine how wide the lake is ? 