Question

a boat goes 20 km upstream and 28 km downstream in 6 hours. it goes 30 km upstream and 21 km downstream in 6.5 hours. find the speed of boat in still water and speed of stream.

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Answer 1

Answer:

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

Let speed of stream = y km/hr

Upstream speed = (x - y) km/hr

Downstream speed = (x + y) km/hr.

Case I :  

x−y

24 +  

x+y

28

=6

Let  

x−y

1 =u &  

x+y

1 =v

24u+28v=6                .....(1)

Case II :  

x−y

30 +  x+y

21  =  2

13

​  

 

30u+21v=  

2

13

​  

    ......(2)

Multiplying eq.(1) by 3 & eq.(2) by 4, we get

72u+84v=18

 120u + 84v = 26

          +48u=−8

u=  

6

1

​  

 & v=  

14

1

​  

 

6

1

​  

=  

x−y

1

​  

,  

14

1

​  

=  

x+y

1

​  

 

x−y=6        ......(3)

x+y=14 ......... (4)

On solving eq. (3) & (4)

x = 10 & y = 4

Hence, speed of boat in still water is 10 kmph.  

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Step-by-step explanation: