Answer with the Explanation:

The speed of man in still water is 9[1/3]
ATQ, time taken while rowing upstream = 3k
Time taken while rowing downstream = k
We know that time is inversely proportional to speed.
Upstream speed (y) = k
Downstream (x) = 3k

Now, apply the formula.

Speed of man in still water = (1/2) [speed of downstream + speed of upstream]

Or, 9[1/3] = (1/2) [3k+ k]
Or, 28/3 = 2k
Or, k = 14/3
So, upstream speed (y) = 14/3
And, downstream speed (x) = (14/3) * 3 = 14

Now, apply the formula.

Speed of current = (1/2) [downstream speed – upstream speed]
= (½) [14 – 14/3]
= 28/6 = 4[2/3]

Answer with the Explanation:

ATQ,

Speed of boat in still water (S_b) = 9km/hr Speed of stream (S_c) = 2.5km/hr Distance against the stream = 9.1 km

Note: against the steam = upstream

Now, apply the formula:

The speed of boat upstream = speed of boat – the speed of the stream

The speed of upstream = 9-2.5 = 6.5km/hr Now, time= Distance/speed Time = 9.1/6.5, or 7/5 Or, time = 1[2/5] Or, 1hr + (2/5)*60 = 1hr + 24minutes

Explanation:

Rate downstream =		16	kmph = 8 kmph.
		2

Rate upstream =		16	kmph = 4 kmph.
		4

Speed in still water =	1	(8 + 4) kmph = 6 kmph.
	2

Answer with the Explanation:

Let the distance between A and B is x km
The velocity of the boat in still water is 4km/hr.
Time taken to upstream and downstream is 3hr

Apply the formula:

Time = distance/speed
And Speed in the downstream = speed of the boat in still water+ speed of the stream
Speed in Upstream = speed of the boat in still water- speed of the stream

Let the speed of stream = y

So, (x/(4+y))+ (x/(4-y)) = 3hr.
We have one equation and two unknown expressions (x and y).
So, the given data is insufficient.

Explanation:

Rate downstream =		1	x 60	km/hr = 6 km/hr.
		10

Rate upstream = 2 km/hr.

Speed in still water =	1	(6 + 2) km/hr = 4 km/hr.
	2

Required time =		5	hrs = 1	1	hrs = 1 hr 15 min.
		4		4

Explanation:

Let man's rate upstream be x kmph.

Then, his rate downstream = 2x kmph.

(Speed in still water) : (Speed of stream) =		2x + x		:		2x - x
		2				2

=	3x	:	x
	2		2

= 3 : 1.

Explanation:

Let the speed of the boat in still water be x kmph. Then,

Speed downstream = (x + 3) kmph,

Speed upstream = (x - 3) kmph.

(x + 3) x 1 = (x - 3) x	3
	2

 2x + 6 = 3x - 9

 x = 15 kmph

Explanation:

We can write three-quarters of a kilometre as 750 metres,

and 11 minutes as 675 seconds.

Rate upstream =		750	m/sec	=	10	m/sec.
		675			9

Rate downstream =		750	m/sec	=	5	m/sec.
		450			3

Rate in still water =	1		10	+	5	m/sec
	2		9		3

=	25	m/sec
	18

=		25	x	18	km/hr
		18		5

= 5 km/hr.

Explanation:

Speed downstream = (15 + 3) kmph = 18 kmph.

Distance travelled =		18 x	12	km = 3.6 km.
			60

Answer with the Explanation:

Let the speed or velocity of the boat in still water is x km/hr
And the Speed of the stream = 5km/hr
So, the speed of the boat along the stream = (x+5) km/hr.
The velocity of the boat against the stream = (x-5) km/hr.

Note: Time = Distance / Speed

So, [10/ (x+5)] + [10/ (x-5)] = (50/60) hrs.

Note: go through the given options to get the answer quickly or solve the equation as follows:

Or, [10 (x-5+x+5)]/ [(x+5) (x-5)] = 5/6
Or, 20x * 6 = 5(x2-52)
Or, 120x = 5(x2-25)
Or, x2-25-24x=0
Or, x2-24x-25=0
Or, x2-25x+x-25=0
Or, x(x-25) +1(x-25) =0
Now, we can say
(X-25)(x+1)= 0
Or, x=25, x= -1 (speed can’t be -ve).
So, the velocity of the boat in still water is 25 km/hr.

Answer with the Explanation:

Let the speed of man in still water (Sb) =5km/hr
And the speed of water/stream (Sc) =1.5km/hr

Time taken to upstream and downstream is 1hr.

Apply the formula:

Time = distance/speed
Downstream speed of the man = speed of man in still water+ speed of the stream
Upstream speed of the man= speed of man in still water- speed of the stream

Let the distance = x km

Now, (x/ downstream speed) + (x/ upstream speed) = time
Or, (x/ (Sb + Sc)) + (x/ (Sb – Sc)) = 1hr
Or, (x/ (5+1.5)) + (x/ (5-1.5)) = 1
Or, (x/6.5) + (x/3.5) = 1
Or, LCM of 6.5 and 3.5 = 45.5
Or, (7x+13x)/ 45.5 = 1
Or, 20x= 45.5
Or, x = 2.275 km
The place is 2.275 km away from the starting point

Explanation: