A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current ?

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 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: 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: 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: 8 and 1 kmph

Explanation:

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

Correct Answer: 2.83 kmph

Explanation:

Given speed of the person = 8 1/2 = 17/2 kmph
Let the speed of the stream = x kmph
speed of upstream = 17/2 - x
speed of downstream = 17/2 + x
But given that,
2(17/2 - x) = 17/2 + x
=> 3x = 17/2
=> x = 2.83 kmph.

Correct Answer: 3 hrs 30 min

Explanation:

Let the speed of boat and stream be x and y kmph respectively.

According to question

d/x+y + d/x-y = 5h 15m or 21/4 hrs ......(i)

and 2d/x-y = 7...... (ii)

From eq. (i) and (ii)

2d/x+y = 7/2

Hence, Amith will take to row 2d km distance downstream in 7/2 hrs

= 3.5 hrs

= 3 hrs 30 min.

Correct Answer: 8:3

Correct Answer: 900 kms

Explanation:

Let the distance he covered each way = d kms

According to the question,

d/45 - d/50 = 1

=> d = 450 kms.

 

Hence, the total distance he covered in his way = d + d = 2 d = 2 x 450 = 900 kms.

Correct Answer: 72 km

Explanation:

Rate of her upstream = 12/2.5 = 4.8 km/hr

Then, ATQ

Rate of downstream = 4.8 x 3 = 14.4 km/hr

 

Hence, the distance she covers downstream in 5 hrs = 14.4 x 5 = 72 kms.