Question

A boat takes 6 hours to travel 8 kms. upstream and 32 kms. downstream and it takes 7 hours to travel 20 kms. upstream and 16 kms. downstream. Find the speed of the boat in still water and the speed of the stream. OR The 10th term of an A.P. is 52 and 16th term is 82. Find the 32nd term of that A.P.

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Answer 1

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