A steamer can row at the speed of 16km/hr in still water. If the river is flowing at 8 km/hr and it takes 12 hours for a round trip, then the distance between the two places is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 72 km
Speed of steamer in still water: $u = 16$ km/hr
Speed of river: $v = 8$ km/hr
Time for round trip: $T = 12$ hours
Let the distance between the two places be $d$ km.
Downstream speed = $u + v = 16 + 8 = 24$ km/hr
Upstream speed = $u - v = 16 - 8 = 8$ km/hr
Time downstream + Time upstream = 12
$\frac{d}{24} + \frac{d}{8} = 12$
$\frac{d}{24} + \frac{3d}{24} = \frac{4d}{24} = \frac{d}{6} = 12$
$d = 72$ km
Distance between the two places = 72 km