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.
\[s = \frac{14 - 6}{2} = 4 \text{ km/hr}\]
\[b = \frac{14 + 6}{2} = 10 \text{ km/hr}\]
Please log in or register to report this question.
A boat covers a distance of 30 km in 2 ½ hours running downstream while returning it covers the same distance in 3 ¾ hours. What is the speed of the boat in still water?
Answer: D
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = \frac{30}{2.5} = 12 \text{ km/hr}, \qquad b - r = \frac{30}{3.75} = 8 \text{ km/hr} \]
\[ b = \frac{12 + 8}{2} = 10 \text{ km/hr} \]
10 km/hr is absent from the options, so the answer is none of these. The 12 and 8 on the list are the downstream and upstream speeds - intermediate values, not the answer.
Please log in or register to report this question.
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 travelled by the man?
Answer: C
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 7.2 \text{ kmph}, \qquad b - r = 4.8 \text{ kmph} \]
\[ \frac{D}{7.2} + \frac{D}{4.8} = 1 \quad\Longrightarrow\quad \frac{5D}{14.4} = 1 \quad\Longrightarrow\quad D = 2.88 \text{ km} \]
That is the one-way distance. The question asks for the total journey, so it must be doubled:
\[ 2 \times 2.88 = 5.76 \text{ km} \]
2.88 km is the correct answer to a different question - how far away the place is.
Please log in or register to report this question.
In a river, a man takes 3 hours in rowing 3 km upstream or 15 km downstream. What is the speed of the current?
Answer: A
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Both legs take 3 hours, so read each speed straight off its distance.
\[ b - r = \frac{3}{3} = 1 \text{ km/hr}, \qquad b + r = \frac{15}{3} = 5 \text{ km/hr} \]
\[ r = \frac{5 - 1}{2} = 2 \text{ km/hr} \]
The boat does 3 km/hr in still water - only slightly faster than the current, which is why the upstream progress is so slow.
Please log in or register to report this question.
Sahil can row 3 km against the stream in 20 minutes and he can return in 18 minutes. What is rate of current ?
Answer: A
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Convert each time to hours and divide into the 3 km.
\[ b - r = \frac{3}{20/60} = 9 \text{ km/hr} \]
\[ b + r = \frac{3}{18/60} = 10 \text{ km/hr} \]
\[ r = \frac{10 - 9}{2} = \frac{1}{2} \text{ km/hr} \]
The current's speed is half the difference of the two, not the difference itself. Sahil rows at 9.5 km/hr in still water.
Please log in or register to report this question.
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.
Please log in or register to report this question.
Michel can swim in still water at the rate of 6km per hour. After swimming in a stream, she realized that she takes twice the time to go upstream as she takes to go downstream. What is speed of the current?
Answer: B
Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
Time is inversely proportional to speed over the same distance, so taking twice as long upstream means going half as fast:
\[ \frac{b + r}{b - r} = 2 \]
\[ 6 + r = 2(6 - r) = 12 - 2r \]
\[ 3r = 6 \quad\Longrightarrow\quad r = 2 \text{ km/h} \]
Checking: downstream 8 km/h and upstream 4 km/h - exactly double.
Please log in or register to report this question.
A man can row three-quarters of a kilometer against the stream in 11 ¼ minutes and return in 7 ½ minutes. The speed of the man in still water is?
Answer: D
Distance covered upstream in 45/4min =3/4 km
Distance covered upstream in 1 hr =(3/4 × 2/15 × 60) km/hr = 4 km/hr
Distance covered downstream in 15/2 min = ¾ km
Distance covered downstream in 1hr
= (3/4 × 2/15 × 60)km/hr = 6 km/hr
Speed of the man in still water
= ½ (6 + 4)km/hr = 5 km/hr
Please log in or register to report this question.
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?
Answer: A
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ \frac{35}{b + 1} + \frac{35}{b - 1} = 12 \]
\[ \frac{35(b - 1) + 35(b + 1)}{b^{2} - 1} = \frac{70b}{b^{2} - 1} = 12 \]
\[ 70b = 12b^{2} - 12 \quad\Longrightarrow\quad 6b^{2} - 35b - 6 = 0 \]
\[ b = \frac{35 + \sqrt{1225 + 144}}{12} = \frac{35 + 37}{12} = 6 \text{ kmph} \]
Checking: 35 km at 7 kmph takes 5 hours and at 5 kmph takes 7 - twelve hours in total.
Please log in or register to report this question.
A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Answer: C
With \( b \) the still-water speed and \( r \) the stream's,
\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]
\[ b + r = 15 + 5 = 20 \text{ kmph} \]
Downstream the current helps, so the speeds add. Upstream they would subtract, giving 10 kmph - which is why 10 is offered as a distractor.
Please log in or register to report this question.
