Question

A boat goes 20km upstream and 28 km down time in 6 hours. It goes 30 km team and 21 km downstream is hours 30 minute Determine the speed of the stream and thus of the boat in still water?​

Answer 1

Let speed of boat in still water be a km/hr.

Let rate of the current be b km/hr.

∴ Speed of the boat upstream =(a−b) km/hr.

∴  

a−b

24

​

+  

a+b

28

​

=6          ...(i)

and  

a−b

30

​

+  

a+b

21

​

=  

2

13

​

          ..(ii)

From (i) and (ii), we have

a−b

1

​

=  

6

1

​

 and  

a+b

1

​

=  

14

1

​

 

⇒a−b=6 and a+b=14

⇒a=10 km/hr.

Answer 2

Answer:

Hope this helps you ❣❣❣

Step-by-step explanation:

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 :- $\frac{20}{x-y} + \frac{28}{x+y} = 6$

Let  $\frac{1}{x-y} = u$ & $\frac{1}{x+y} = v$

∴ 20u + 28v = 6  ---------(1)

Case II :- $\frac{30}{x-y} + \frac{21}{x+y} = \frac{13}{2}$

∴ $30u + 21v =$ $\frac{13}{2}$ -----------(2)

Multiplying (1) by 30 and (2) by 20,

60u + 840v = 180 --------(3)

60u + 420v = 130 --------(4)

After simplifying (3) and (4),

420v = 50

v = 50 / 420

v = 5 / 42

60u + 420 ( 5 / 42 ) = 130

60u + 50 = 130

60u = 130 - 50

u = 80 / 60

u = 4 / 3

5 / 42 = 1 / x+y  &  4 / 3 = 1 / x-y

5 (x + y) = 42         4 (x - y) = 3

x + y = 42 / 5         x - y = 3 / 4

2x = 42 / 5 + 3 / 4

2x = (168 + 15) / 20

2x = 183 / 20

x = 183 / 40

x = 4.575 & y = 3.825

Speed of the stream = 3.825 km/hr

Speed of boat in still water = 4.575 km/hr

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