A man's speed with the current is 20 kmph and speed of the current is 3 kmph. The Man's speed against the current will be
Answer: C
Speed with current is 20,
speed of the man + It is speed of the current
Speed in still water = 20 - 3 = 17
Now speed against the current will be
speed of the man - speed of the current
= 17 - 3 = 14 kmph
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A boat can travel with a speed of 16 km/hr in still water. If the rate of stream is 5 km/hr, then find the time taken by the boat to cover distance of 84 km downstream.
Answer: A
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 16 + 5 = 21 \text{ km/hr} \]
\[ t = \frac{84}{21} = 4 \text{ hours} \]
Using the still-water speed of 16 km/hr would give 5.25 hours - the stream is helping, so the trip must take less than that.
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A man can row at 5 kmph in still water. If the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back. how far is that place.
Answer: C
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 6 \text{ km/h}, \qquad b - r = 4 \text{ km/h} \]
\[ \frac{D}{6} + \frac{D}{4} = 1 \]
\[ D\left(\frac{2 + 3}{12}\right) = 1 \quad\Longrightarrow\quad \frac{5D}{12} = 1 \]
\[ D = 2.4 \text{ km} \]
Using 5 km/h both ways would give 2.5 km. The current always costs time overall, so the true distance covered in the hour is a little less.
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A man rows to a place 48 km away and back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against it. What is the speed of the stream ?
Answer: B
Correct answer: 1 km/hr
Equal times over 4 km downstream and 3 km upstream give \(\tfrac{4}{d} = \tfrac{3}{u}\), so \(u = \tfrac{3d}{4}\).
\[\frac{48}{d} + \frac{48}{u} = 14 \quad\Longrightarrow\quad \frac{48}{d} + \frac{64}{d} = 14 \quad\Longrightarrow\quad \frac{112}{d} = 14\]
So \(d = 8\) and \(u = 6\), giving \(s = \tfrac{8-6}{2} = 1\) km/hr.
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The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance traveled downstream in 12 minutes is:
Answer: C
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 20 + 5 = 25 \text{ km/h} \]
\[ 12 \text{ min} = \frac{12}{60} = 0.2 \text{ h} \]
\[ \text{distance} = 25 \times 0.2 = 5 \text{ km} \]
Using the still-water speed of 20 km/h instead would give 4 km - the current is helping, so the distance must exceed that.
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A boat covers 36 km downstream in 3 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water ?
Answer: A
Correct answer: 9 km/hr
\[\text{Downstream speed} = \frac{36}{3} = 12 \text{ km/hr}, \qquad \text{Upstream speed} = \frac{36}{6} = 6 \text{ km/hr}\]
The still-water speed is the average of the two, since the stream adds to one and subtracts from the other:
\[b = \frac{12 + 6}{2} = 9 \text{ km/hr}\]
The same pair gives the stream speed as \(\tfrac{12-6}{2} = 3\) km/hr.
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In one hour a boat goes 14 km along the stream and 6 km against it. What is the speed of the stream ?
Answer: A
Correct answer: 4 km/hr
The two figures are the downstream and upstream speeds directly, since each is covered in one hour.
\[s = \frac{14 - 6}{2} = 4 \text{ km/hr}\]
\[b = \frac{14 + 6}{2} = 10 \text{ km/hr}\]
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A man can row a boat three quarters of a kilometer in 11.25 minutes. What is the speed of the boat in still water?
Answer: C
Convert both quantities to the units the answer is wanted in.
\[ 11.25 \text{ min} = \frac{11.25}{60} = 0.1875 \text{ h} \]
\[ \text{speed} = \frac{0.75}{0.1875} = 4 \text{ km/h} \]
Equivalently, three quarters of a kilometre in \( \tfrac{3}{16} \) of an hour means \( \tfrac{3}{4} \times \tfrac{16}{3} = 4 \) km/h. No current is mentioned, so this speed is the still-water speed.
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A boat takes 4 hours to travel 24 km downstream and 6 hours to return. What is the speed of the current ?
Answer: C
Correct answer: 1 km/hr
\[\text{Downstream} = \frac{24}{4} = 6 \text{ km/hr}, \qquad \text{Upstream} = \frac{24}{6} = 4 \text{ km/hr}\]
\[s = \frac{6 - 4}{2} = 1 \text{ km/hr}\]
The boat itself moves at \(\tfrac{6+4}{2} = 5\) km/hr in still water.
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A boat can travel at 15 km/hr in still water. If the stream flows at 5 km/hr, how long will the boat take to cover 60 km upstream ?
Answer: C
Correct answer: 6 hours
Against the stream the speeds subtract:
\[\text{Upstream speed} = 15 - 5 = 10 \text{ km/hr}\]
\[\text{Time} = \frac{60}{10} = 6 \text{ hours}\]
The same 60 km downstream, at 20 km/hr, would take only 3 hours.
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