I think the question is ambiguous.

There are three solutions:

1. When both A and B touches the other shore atleast once.

2. When A touches the other shore and B did not even reach the other shore

3. When B touches the other shore and A did not even reach the other shore

1. 500/a = x-500/b i.e a/b = 500/(x-500)

(2x-300)/b = (x+300)/a i.e a/b =

Solving these two we get x = 1200

2. 500/a = x-500/b i.e a/b = 500/(x-500)

(x+300)/a = 300/b i.e a/b = (x+300)/300

Solving these two we get x = 100(1+SQRT(31))

3. 500/a = x-500/b i.e a/b = 500/(x-500)

(2x-300)/b = (x-300)/a i.e a/b = (x-300)(2x-300)

Solving these two we get x = 100(7+SQRT(19))

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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008