Question

A boat can row 1 km with stream in 10 minutes and 1 km against stream in 20 minutes. what is the speed of the boat in stll water? a.1.5 km/hr b.3 km/hr c.3.4 km/hr d.4.5 km/hr​

Answer 1

Concept: A boat can row 1km in 10 min along the stream (downstream) and 1km against the stream in 20 min (upstream). Now, while traveling upstream, the time taken will be more than downstream because the body travels against gravity. Also, the speed of the boat is always greater than the speed of the stream.

Assumption: Let the speed of the boat be (x) km/hr and the speed of the stream be (y) km/hr.

Note: For traveling upstream, the net speed will be (x - y) km/hr and for traveling downstream, the net speed will be (x + y) km/hr.

We know that,

• Speed = distance / time

We will substitute the given values in the above formula and find the values of x (speed of the boat in still water, where the speed of the stream is 0).

Case 1 (traveling upstream)

$\\ \quad\longrightarrow\quad \rm x - y = \dfrac{1}{10/60}$

$\\ \quad\longrightarrow\quad \rm x - y = \dfrac{60}{10}$

$\\ \quad\longrightarrow\quad \rm x - y = 6 - - - (i)$

Case 2 (traveling downstream)

$\\ \quad\longrightarrow\quad \rm x + y = \dfrac{1}{20/60}$

$\\ \quad\longrightarrow\quad \rm x + y = \dfrac{60}{20}$

$\\ \quad\longrightarrow\quad \rm x + y = \dfrac{6}{2}$

$\\ \quad\longrightarrow\quad \rm x + y = 3 - - - (ii)$

Now, add equations (i) as well as (ii) in order to eliminate y.

$\\\quad\mapsto\quad\rm x-y+x+y= 6 + 3$

$\\\quad\mapsto\quad\rm 2x= 9$

$\\\quad\mapsto\quad\rm x= \dfrac{9}{2}$

$\\\quad\therefore\quad \boxed{\rm x= 4.5 \: km/hr}\bigstar$

Hence, option (d) is right

______________________________

Answer 2

Given :  A boat can row 1 km with stream in 10 minutes and

1 km against stream in 20 minutes.

To Find : The speed of the boat in still water?

a.1.5 km/hr b.3 km/hr c.3.4 km/hr d.4.5 km/hr​

Solution:

Distance = speed * time

10 mins = 10/60 hrs

20 mins = 20 /60 hrs

speed of the boat in still water = x  km/hr

speed of the stream = y  km/hr

speed of the boat  with stream = x + y km/hr

x + y   = 1/(10/60)  

=> x + y  = 6

speed of the boat against stream = x - y km/hr

x + y   = 1/(20/60)  

=> x - y  = 3

Adding both

=> 2x = 9

=> x = 4.5

The speed of the boat in still water is 4.5 km/hr

Correct option is d) 4.5 km/hr

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