Question

A boat goes 30 km downstream and 36 km upstream in 6 hours. It takes 5 hours to go 45

km downstream and 18 km upstream. Determine the speed of the stream and the speed of the

boat in still water.x​

Answer 1

Step-by-step explanation:

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Let the speed of the boat in still water be x km/hr

Let the speed of the stream be y km/hr

The speed of the boat downstream = (x+y) km/hr

The speed of the boat upstream = (x−y) km/hr

Time=

Speed

Distance

6 hours to travel 8 km upstream and 32 km downstream,

i. e 6=

x−y

8

+

x+y

32

(1)

7 hours to travel 20 km upstream and 16 km downstream.

i.e 7=

x−y

20

+

x+y

16

(2)

Let

x−y

1

=a and

x+y

1

=b

∴6=8a+32b ...(3)

7=20a+16b ...(4)

On solving the equations, we get a=

4

1

and b=

8

1

x−y

1

=

4

1

and

x+y

1

=

8

1

⟹4=x−y

⟹8=x+y

Add the above (2) eqn we get

12=2x

x=6 and y=2

So, the speed of the boat in still water = 6 km/hr

The speed of the stream = 2 km/hr