99+ Boats and Streams Problems With Solutions And Explanation

Q:

A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C which is at midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?

A) 180 km	B) 160 km
C) 140 km	D) 120 km

Answer & Explanation Answer: A) 180 km

Explanation:

Speed in downstream = (14 + 4) km/hr = 18 km/hr;

Speed in upstream = (14 – 4) km/hr = 10 km/hr.

Let the distance between A and B be x km. Then,

x/18 + (x/2)/10 = 19 ⇔ x/18 + x/20 = 19 ⇒ x = 180 km.

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Q:

A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.

A) 12 km/hr, 3 km/hr	B) 9 km/hr, 3 km/hr
C) 8 km/hr, 2 km/hr	D) 9 km/hr, 6 km/hr

Answer & Explanation Answer: B) 9 km/hr, 3 km/hr

Explanation:

Let the speed of the boat = p kmph

Let the speed of the river flow = q kmph

From the given data,

$2 x \frac{28}{p + q} = \frac{28}{p - q}$

=> 56p - 56q -28p - 28q = 0

=> 28p = 84q

=> p = 3q.

Now, given that if

$\frac{28}{3 q + 2 q} + \frac{28}{3 q - 2 q} = \frac{672}{60} = > \frac{28}{5 q} + \frac{28}{q} = \frac{672}{60} = > q = 3 kmph = > x = 3 q = 9 kmph$

Hence, the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.

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Q:

The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is ?

A) 8 kmph	B) 6 kmph
C) 7.5 kmph	D) 5.5 kmph

Answer & Explanation Answer: B) 6 kmph

Explanation:

Speed of the stream = 1
Motor boat speed in still water be = x kmph
Down Stream = x + 1 kmph
Up Stream = x - 1 kmph
[35/(x + 1)] + [35/(x - 1)] = 12
x = 6 kmph

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Q:

A boat sails 15 km of a river towards upstream in 5 hours. How long will it take to cover the same distance downstream, if the speed of current is one-fourth the speed of the boat in still water:

A) 1.8h	B) 3h
C) 4h	D) 5h

Answer & Explanation Answer: B) 3h

Explanation:

Upstream speed = B-S

Downstream speed = B+s

B-S = 15/5 = 3 km/h

Again B= 4S

Therefore B-S = 3= 3S

=> S = 1 and B= 4 km/h

Therefore B+S = 5km/h

Therefore, Time during downstream = 15/5 = 3h

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Q:

A boy can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is ?

A) 1.8 kmph	B) 2 kmph
C) 2.2 kmph	D) 1.5 kmph

Answer & Explanation Answer: D) 1.5 kmph

Explanation:

Speed of Boy is B = 4.5 kmph

Let the speed of the stream is S = x kmph

Then speed in Down Stream = 4.5 + x

speed in Up Stream = 4.5 - x

As the distance is same,

=> 4.5 + x = (4.5 - x)2

=> 4.5 + x = 9 -2x

3x = 4.5

x = 1.5 kmph

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Q:

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?