11) The velocity of a boat in still water is 9 km/hr, and the speed of the stream is 2.5 km/hr. How much time will the boat take to go 9.1 km against the stream?

Upstream speed = distance covered in upstream/ time Downstream speed = distance covered in downstream/ time

Upstream speed = 40/8 = 5kmph Downstream speed = 36/6 = 6kmph Now, speed of man in still water= (½) [speed in downstream + speed in upstream]

Or, the speed of man = [½][6+5] =5.5kmph

13) A boat travels upstream from Q to P and downstream from P to Q in 3 hours. If the distance between P to Q is 4km and the speed of the stream is 1kmph, then what is the velocity of the boat in still water?

Let the velocity or speed of the boat in still water is x km/hr. And the Speed of the stream = 1km/hr So, the speed of the boat along the stream = (x+1) km/hr. The speed of the boat against the stream = (x-1) km/hr.

Note: time = Distance / Speed

So, [4/ (x+1)] + [4/ (x-1)] = 3 hrs.

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

Or, [4 (x+1+x-1)]/ [(x+1) (x-1)] = 3 Or, 8x = 3(x2-12) Or, 8x = 3×2-3 Or, 3×2-8x-3=0 Or, 3×2- 9x+ x-3 = 0 Or, (x-3) (3x+1) = 0 Therefore x=3 or, x=-1/3 (speed can’t be -ve) Hence, the speed or velocity of the boat in still water is 3 km/hr.

14) The speed of the stream is 5km/hr. A boat goes 10 km upstream and returns back to the starting point in 50 minutes. Find the velocity of the boat in still water.

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.

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15) A boat travels from A to B along the stream and from B to A against the stream in 3 hours. If the velocity of the boat in still water is 4 km/hr, what is the distance between A and B?

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.

16) A man can row, 5km/hr in still water and the velocity of the stream is 1.5 km/hr. He takes an hour when he travels upstream to a place and returns back to the starting point. How far is the place from the starting point?

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.

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17) A boatman can row a certain distance down the stream in 2 hours and can row the same distance up the stream in 3 hours. If the velocity of the stream is 4km/hr, what is the speed of the boat in still water?

Let the distance = x km Time is taken in downstream = 2 hour So, the speed of downstream is x/2 km/hr Similarly, the time is taken in upstream = 3 hr So, the speed of upstream is x/3 km/hr Speed of stream = 4 km/hr

Now, apply the formula.

Speed of stream = (1/2) [speed of downstream – speed of upstream] Or, 4 = (1/2) [x/2 – x/3] Take LCM of 2 and 3 = 6 Now, (½) [(3x-2x)/6] = 4 Or, x= 48 km

Now, speed of downstream = 48/2 = 24 km/hr And the speed of upstream = 48/3 = 16km/hr

Now, apply the formula.

Speed of boat in still water = (½) [24+16] = 20km/hr

18) A man can row 9[1/3] km/hr in still water. He finds that it takes thrice as much time to row upstream as to row downstream (same distance). Find the speed of the current.

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]

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

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19) A boat covers 6 km upstream and returns back to the starting point in 2 hours. If the flow of the stream is 4 km/hr, what is the speed of the boat in still water?

ATQ, distance covered in upstream = 6 km, and the same distance is covered in downstream

Now, apply the formula

Time = Distance/ speed

Let the upstream speed = y km/hr, and the downstream speed = x km/hr. Or, (6/x) + (6/y) = 2 Or, speed in upstream = speed of boat in still water – speed of stream Or, speed in downstream = speed of boat in still water + speed of stream Let S_{b}= speed of boat in still water

20) A boat covers 12 km upstream and 18km downstream in 3 hours while it covers 36km upstream and 24 km downstream in 6[1/2] hours, what is the velocity of the stream?