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 ?

• A. km
• B. $4\frac{1}{2}$$ km
• C. $5\frac{1}{2}$$ km
• D. $6\frac{1}{2}$$ km