Question : A boat moves downstream at the rate of 1 km in $7\frac{1}{2}$ minutes and upstream at the rate of 5 km an hour. What is the speed of the boat in the still water?
Option 1: $3\frac{1}{2}$ km/hr
Option 2: $6\frac{1}{2}$ km/hr
Option 3: $4$ km/hr
Option 4: $8$ km/hr
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Correct Answer: $6\frac{1}{2}$ km/hr
Solution : Given: Downstream Speed = 1 km in $7\frac{1}{2}$ minutes = $\frac{1}{\frac{15}{2×60}}$ = 8 km/hr Upstream Speed = 5 km/hr Speed of boat in still water = $\frac{\text{(Downstream Speed + Upstream Speed)}}{2}$ = $\frac{8+5}{2}$ = $6\frac{1}{2}$ km/hr Hence, the correct answer is $6\frac{1}{2}$ km/hr.
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