Question

The speed of the boat in still water is 20 km/hr. It can go 15 km upstream and return downstream to the original point in 2 hours. Find the speed of the stream.​

Answer 1

Answer:

Step-by-step explanation:

Given :

Speed of boat in still water =15 km/hr  

Let x be speed of the stream in km/hr

Speed of the boat upstream =15−x

Speed of the boat down stream =15+x

Time taken for upstream T  

1

​

=  

15−x

30

​

 

Time taken for downstream T  

2

​

=  

15+x

30

​

 

Given, T  

1

​

+T  

2

​

=  

2

9

​

 

=  

15−x

30

​

+  

15+x

30

​

=  

2

9

​

 

=30(  

15−x

1

​

+  

15+x

1

​

)=  

2

9

​

 

=30(  

(15−x)(15+x)

15+x÷15−x

​

)=  

2

9

​

 

=  

225−x  

2

 

30×30

​

=  

2

9

​

 

=  

225−x  

2

 

100

​

=  

2

1

​

⇒225−x  

2

=200

⇒x  

2

=25

⇒x=5 ....(∵x is +ve)

⇒x=5 km/hr

Speed of the stream =5 km/hr.

Answer 2

Answer :-

Given :-

Speed of boat in still water = 20 km/hr

Let x be speed of the stream in km/hr

Speed of the boat upstream = 20 − x

Speed of the boat down stream = 20 + x

Time taken for upstream T1 =

$\frac{15}{20 - x}$

Time taken for downstream T2=

$\frac{15}{20 + x}$

Now ,

T1 + T2 = 2 ( because it returns to the original point in 2 hours )

$\frac{15}{20 - x} + \frac{15}{20 + x } = 2$

$15 \: ( \frac{1}{20 - x } + \frac{1}{20 + x} ) = 2$

$15 \: ( \frac{20 + x + 20 - x}{(20 - x)(20 + x)} ) \: = 2$

$\frac{15 \times 40}{400 - {x}^{2} } = 2$

$800 \: - 2 {x}^{2} = 600$

$2 {x}^{2} = 200$

${x}^{2} = 100$

$x \: = 10 \: ( \: x \: is \: positive)$

Speed of the stream = 10 km/hr.