A boat can row at the speed of 16 km/hr in still water. If the river is flowing at 8 km/hr, and it takes 8 hours for a round trip, then the distance between the two places is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 48 km
Let the distance between the two places be $d$ km.
Speed of boat in still water: $v_b = 16$ km/hr
Speed of river: $v_r = 8$ km/hr
Downstream speed: $v_{down} = v_b + v_r = 16 + 8 = 24$ km/hr
Upstream speed: $v_{up} = v_b - v_r = 16 - 8 = 8$ km/hr
Time for round trip = 8 hours
Time = distance/speed → $\frac{d}{24} + \frac{d}{8} = 8$
$\frac{d}{24} + \frac{d}{8} = 8$
$\frac{d + 3d}{24} = 8 \Rightarrow \frac{4d}{24} = 8 \Rightarrow \frac{d}{6} = 8 \Rightarrow d = 48$ km
Distance between the two places = 48 km