Speed in still water = Average of Speed in Upstream and speed in Downstream
= 1/2 (12 + 6) kmph = 9 kmph.
As the distance travelled is constant, the time taken is inversely proportional to speed.
Let 'u' be the speed of the current and 'v' be the speed of the boat.
Speed of the boat downstream = v + u & upstream = v - u
=> v+u/v-u = 30/20 => v/u = 5 => v = 5u
=> v + u = 6u = 10/20/60 miles/hr
=> 6u = 30 m/h
=> u = 5 m/h
Let the distance be d.
=> 2d = 120
=> d = 60 kms.
Let the speed of the stream = x kmph
From the given data,
=> x = 3 kmph
Therefore, the speed of the stream = 3 kmph
Let the speed of the boat upstream be p kmph and that of downstream be q kmph
Time for upstream = 8 hrs 48 min = hrs
Time for downstream = 4 hrs
Distance in both the cases is same.
=> p x = q x 4
=> 44p/5 = 4q
=> q = 11p/5
Now, the required ratio of Speed of boat : Speed of water current
=
=> (11p/5 + p)/2 : (11p/5 - p)/2
=> 8 : 3
Speed in still water = 6 kmph
Stream speed = 1.2 kmph
Down stream = 7.2 kmph
Up Stream = 4.8 kmph
x/7.2 + x/4.8 = 1
x = 2.88
Total Distance = 2.88 x 2 = 5.76 kms
Let Speed of boat in still water = b
Let Speed of still water = w
Then we know that,
Speed of Upstream = U = boat - water
Speed of Downstream = D = boat + water
Given, U + D = 82
b - w + b + w = 82
2b = 82
=> b = 41 kmph
From the given data,
41 - w = 105/3 = 35
w = 6 kmph
Now,
b + w = 126/t
=> 41 + 6 = 126/t
=> t = 126/47 = 2.68 hrs.
Downstream speed = 72km/8hrs = 9 kmph
upstream speed = 84km/12hrs = 7 kmph
speed of boat = avg of downstream and upstream speeds
speed of boat = (9+7)/2kmph = 8 kmph.
current speed = half of the difference of downstream and upstream speeds
currend speed = (9-7)/2kmph = 1 kmph
Speed in downstream = 96/8 = 12 kmph
Speed of current = 4 km/hr
Speed of the boatman in still water = 12 ? 4 = 8 kmph
Speed in upstream = 8 ? 4 = 4 kmph
Time taken to cover 8 km upstream = 8/4 = 2 hours.
Let the distance in one direction = k kms
Speed in still water = 4.5 kmph
Speed of river = 1.5
Hence, speed in upstream = 4.5 - 1.5 = 3 kmph
Speed in downstream = 4.5 + 1.5 = 6 kmph
Time taken by Rajesh to row upwards = k/3 hrs
Time taken by Rajesh to row downwards = k/6 hrs
Now, required Average speed =
Therefore, the average speed of the whole journey = 4kmph.
Speed of the boat upstream = 36/9 = 4 kmph
Speed of the boat in downstream = 36/6 = 6 kmph
Speed of stream = 6-4/2 = 1 kmph
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