A boat travels 72 km downstream in 8 hours and 84 km upstream in 12 hours. Find the speed of the boat in still water and the speed of the water current ?

Correct Answer: 2.7 hrs

Explanation:

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.

Correct Answer: 9

Explanation:

Speed in still water = Average of Speed in Upstream and speed in Downstream

= 1/2 (12 + 6) kmph = 9 kmph.

Correct Answer: 5 m/h

Explanation:

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

Correct Answer: 60 kms

Explanation:

Let the distance be d.

  d 8 - 2 - d 8 + 2 = 4

 

=> 2d = 120 

 

=> d = 60 kms.

Correct Answer: 3 kmph

Explanation:

Let the speed of the stream = x kmph

 

From the given data,

 

  12 9 + x + 12 9 - x = 3 h r s

3 x 2 = 27

 

=> x = 3 kmph

 

Therefore, the speed of the stream = 3 kmph

Correct Answer: 2 hrs

Explanation:

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.

Correct Answer: 4 kmph

Explanation:

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 = $$\begin{gathered} Total distance Total speed = 2 k k 3 + k 6 \\ = 2 k x 18 6 k + 3 k = 4 kmph \end{gathered}$$ 

 

Therefore, the average speed of the whole journey = 4kmph.

Correct Answer: 1 kmph

Explanation:

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

Correct Answer: 5:1

Explanation:

Let the speed of the man in still water = p kmph

Speed of the current = s kmph

Now, according to the questions

(p + s) x 10 = (p - s) x 15

2p + 2s = 3p - 3s

=> p : s = 5 : 1

 

Hence, ratio of his speed to that of current = 5:1.

Correct Answer: 1.5 kmph

Explanation:

72 --- 9
? ---- 1

=> Down Stream = 8

45 ---- 9 
? ---- 1

=> Up Stream = 5

Speed od current S = ?

S = (8 - 5)/2 = 1.5 kmph.