Boats and Streams Questions and Answers

Rowing speed of Alex in still water=  (Rate upstream+ Rate Downstream)

= \frac{7 + 3}{2}= 5 kmph

And rate of the current= \frac{7 - 3}{2}= 2 kmph

Since it is mentioned that his speed downstream is twice that of the upstream.

So let Sam’s speed upstream be ‘a’ then his speed downstream= 2a

Therefore  \frac{2a + a}{2}= 10 or a= 6.66 kmph

Hence his speed upstream= 6.66 kmph and

His speed downstream= 6.66*2= 13.33 kmph

Therefore the rate of the current= 3.33 kmph

Speed upstream = \frac{4}{\frac{12}{60}}= 20 km/hr
Speed of the stream = 2 km/hr
Speed of boat in still water = (20+2) = 22 km/hr

Let the speed of the boat be ‘a’ (in still water)

Therefore speed downstream= a+2

And speed upstream= a-2

Time taken to cover 10 km back and forth= \frac{10}{a+2} + \frac{10}{a-2}= 40/60

= a²-30a-4= 0

Solving the above equation we get a = 30.13

Speed of the boat with the stream= 6+2= 8 kmph

Therefore time taken by Sam to Cover 36 km= \frac{36}{8}= 4.5 hours

Speed Downstream= 2/20 * 60 = 6 kmph

Speed Upstream= 4/2= 2 kmph

Speed in stable water= \frac{6 + 2}{2}= 4 kmph

Hence time taken t cover 10 km= 10/4 =  2.5 hrs

Let the speed of the boat in still water be

Sam takes 12.5 minutes 750 seconds to cover 900 m upstream

Therefore speed upstream= 900/750 = 1.2 mps

As the time taken downstream 7.5 min or 450 sec

Therefore speed downstream = 900/450= 2 mps

Therefore speed in stable water= 1/2 * (1.2+2)= 1.6 mps

Or 1.6* (3600/1000) = 1.6 * 18/5= 5.76 kmph

Speed of the boat upstream= 4.5-3= 1.5 kmph

Speed of the boat downstream= 4.5+3= 7.5 kmph

Therefore total time taken=\frac{7.5}{1.5} + \frac{7.5}{7.5}= 5 + 1 = 6 hrs

Let Sam’s speed upstream be a kmph

Speed downstream= 3a kmph

Therefore the speed of the boat in still water: Speed of river stream

= \frac{3a +a}{2}:\frac{3a - a}{2}

=  \frac{4a}{2}:\frac{2a}{2}Or 2: 1

Let time taken to cover 8 km be a

Then speed downstream= \frac{8}{a}

And speed upstream= \frac{6}{a} kmph

Therefore \frac{24}{\frac{8}{a}}+\frac{24}{\frac{6}{a}}= 7

Or a= 1 h

Therefore speed downstream= 8/1 and speed upstream= 6/1

Hence rate of stream= \frac{8-6}{2} = 2/2 = 1

Velocity of boat= 13 kmph

Velocity of stream= 5 kmph

Time= 20 hours

Velocity of boat downstream= Velocity of boat+ Velocity of stream

= 13+5= 18 kmph

Velocity of boat upstream= Velocity of boat- Velocity of stream

= 13-5= 8 kmph

The distance between P and Q be S

\frac{S}{8}+0.5\frac{S}{13}= 20

= \frac{13S+4S}{104}= 20

= 17S= 2080

Therefore S= 2080/17= 122.4 kmph