Boats and Streams – Aptitude 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

Given: Speed of Boat in Still Water = 5 km/h Time taken upstream = 2 hours Distance upstream = 10 km Time taken downstream = 1.5 hours Distance downstream = 12 km

First, let's calculate the speed of the boat in the upstream and downstream directions:

Speed Upstream = Distance Upstream / Time Upstream Speed Upstream = 10 km / 2 hours Speed Upstream = 5 km/h

Speed Downstream = Distance Downstream / Time Downstream Speed Downstream = 12 km / 1.5 hours Speed Downstream = 8 km/h

Now, use the formula to calculate the speed of the stream:

Speed of Stream = (Speed Downstream - Speed Upstream) / 2 Speed of Stream = (8 km/h - 5 km/h) / 2 Speed of Stream = 3 km/h / 2 Speed of Stream = 1.5 km/h

So, the speed of the stream is 1.5 km/h.