-A stream is flowing at a speed of 3 km/h. A boat with a speed of 9 km/h is taken downstream in 3×1÷2 hours.
(i) How much distance is covered by the boat?
(ii) How long will the boat take to come back to the starting point?
Answers
Speed of stream, v = 3 kmph
Speed of boat, u = 9 kmph
Downstream speed = u + v = 12 kmph
Upstream Speed = u - v = 6 kmph
Distance = Speed * Time
case (i)If time is 3/2 = 1.5 hrs
case (ii) if time is 3+1/2 = 3.5 hrs
(since the question not clear I took it as two cases.)
case (I)
Downstream distance = 12 * 1.5 = 18 km
To travel back to starting point boat has to travel in Upstream.
upstream distance = 18 km
upstream Speed = 6 kmph
Upstream time = 18/6 = 3 hr
Total distance covered = upstream distance + downstream distance = 18 + 18 = 36 km
Total distance covered = upstream distance + downstream distance = 18 + 18 = 36 kmTotal time = downstream time + upstream time = 1.5 + 3 = 4.5 hr
case (ii)
Downstream distance = 12 * 3.5 = 42 km
To travel back to starting point boat has to travel in Upstream.
upstream distance = 42 km
upstream Speed = 6 kmph
Upstream time = 42/6 = 7 hr
Total distance covered = upstream distance + downstream distance = 42 + 42 = 84 km
Total distance covered = upstream distance + downstream distance = 42 + 42 = 84 kmTotal time = downstream time + upstream time = 3.5 + 7 = 10.5 hr