A man can walk uphill at the rate of \(2\frac{1}{2}\) km/hr and downhill at the rate of \(3\frac{1}{4}\) km/hr. If the total time required to walk a certain distance up the hill and return to the starting point was 4 hr 36 min, then what was the distance walked up the hill by the man ?
4 km
\(4\frac{1}{2} \)km
\(5\frac{1}{2}\) km
\(6\frac{1}{2}\)km
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