Boats & Streams Questions and Answers

Answer: A

Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

Equal times mean the two distances are in the same ratio as the two speeds.

\[ \frac{26}{b + 3} = \frac{14}{b - 3} \]

\[ 26(b - 3) = 14(b + 3) \quad\Longrightarrow\quad 26b - 78 = 14b + 42 \]

\[ 12b = 120 \quad\Longrightarrow\quad b = 10 \text{ km/h} \]

Checking: 26 km at 13 km/h and 14 km at 7 km/h both take exactly 2 hours.

Answer: D

Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

\[ b + r = 30 + 6 = 36 \text{ km/h} \]

\[ 24 \text{ min} = \frac{24}{60} = 0.4 \text{ h} \]

\[ \text{distance} = 36 \times 0.4 = 14.4 \text{ km} \]

Converting the minutes to hours before multiplying is the whole trick; leaving 24 in place would give 864 km - which is why 864 m appears as a distractor.

Answer: A

With \( b \) the still-water speed and \( r \) the stream's,

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

\[ b = \frac{(b+r) + (b-r)}{2}, \qquad r = \frac{(b+r) - (b-r)}{2} \]

\[ r = \frac{35 - 25}{2} = 5 \text{ kmph} \]

The current's speed is half the difference, not the difference itself: it helps by \( r \) one way and hinders by \( r \) the other, so the gap between the two speeds is \( 2r \). That is why 10 kmph is on the list.

Answer: C

Speed of the boat in still water: 15 km/hr

Speed of boat downstream: (15+x)km/hr where x is speed of the current.

The boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.

Total time= Time taken to travel downstream + Time taken to travel upstream

=> 4/5= (30/(15+x))+(30/(15-x))

=>x= 5

Answer: B

Correct answer: 4 hours

Going with the stream the two speeds add:

\[\text{Downstream speed} = 10 + 2 = 12 \text{ km/hr}\]

\[\text{Time} = \frac{48}{12} = 4 \text{ hours}\]

The same journey upstream, at 8 km/hr, would take 6 hours.

Answer: B

Let the rate of the stream be x km/hr. 

Then Speed downstream = (15/2 + x)km/hr. 

Speed upstream = (15/2 -x)km/hr 

(15/2 + x) = 2 (15/2 - x) 

=> 3x =15/2 

=> x = 15/6 = 5/2 = 2.5 

Therefore, Rate of stream = 2.5 km/hr

Answer: D

Let Speed upstream = x km/hr 

Speed downstream = 3x km/hr 

Speed in still water = ½ (x+3x) km/hr = 2x km/hr 

Speed of current = ½ (3x-x) km/hr = x km/hr 

2x = 28/3 or x = 14/3 = 4 2/3 km/hr

Answer: D

Let the distance between the two parts be x km. 

Then speed downstream = x/4 km/hr. 

Speed Upstream = x/5 km/hr 

Speed of the stream = ½ (x/4 -x/5) 

Therefore, ½(x/4 -x/5) = 2. => x/4 -x/5 = 4 => x = 80. 

Hence, the distance between the two ports is 80km.

Answer: A

Write \( b \) for the boat's speed in still water and \( r \) for the stream's. Then

\[ \text{downstream} = b + r, \qquad \text{upstream} = b - r \]

\[ b + r = 12 \text{ km/h}, \qquad b - r = 8 \text{ km/h} \]

The upstream trip takes 4 hours longer over the same distance \( D \):

\[ \frac{D}{8} - \frac{D}{12} = 4 \]

\[ D\left(\frac{3 - 2}{24}\right) = 4 \quad\Longrightarrow\quad \frac{D}{24} = 4 \]

\[ D = 96 \text{ km} \]

Checking: 12 hours upstream against 8 hours downstream - a difference of exactly 4.

Answer: B

x = 7 km/hr ; y = 3 km/hr
Ds = 10 km/hr ; Us = 4 km/hr
Distance (d) is same. Therefore, if time taken for downstream is t hours, the time for upstream is (t + 6) hours.
10*t = 4*(t + 6)
6t = 24 ; t = 4 hours
d = 10*4 = 40 km