Question

A boat covers 32 km upstream and 36 km downstream in 7 hours. In 9 hours, it can cover 40
km upstream and 48 km down-stream. Find the speed of the stream and that of the boat in still water

Answer 1

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

and let the Speed of the stream be ' y '  km/h.

→ Relative speed of the boat in downstream :

= ( x + y ) km/hr

Distance travelled = d_1 = 36

Time = ' t_1 h '

t_1 = d_1 / s_1

t_1 = 36/ x + y

Now,

Relative speed of the boat in upstream

= ( x - y ) km/h

• Distance = d_2

          = 32 km

• Time = t_2

t_2 = 32/ x - y

Hence,

Total time taken is 7 hr

So,

t_1 + t_2 = 7h

36 / ( x + y ) + 32/ ( x - y ) = 7 ____________ ( ! )

→ second time :

Relative speed of the boat in downstream = ( x + y ) km/h

→ d_3 = 48 km

→ Time = t_3

t3 = 48/ ( x + y )

In upstream :

Relative speed of the boat = ( x - y ) km/h

→ Time = t_4 hr

→ d_4 = 40km

t4 = 40/ ( x - y )

Total time = 9 h

48 / ( x + y ) + 40/ ( x - y ) = 9 _______________ ( !! )

Let 1 / ( x + y ) = a ,

1 / ( x - y ) = b

Then,

Rewrite ( ! ) and ( !! ).

we get,

36a + 32 b = 7 ______________ ( !!! )

48a + 40b = 9 ___________ ( !!!! )

Multiply ( !!!! ) by  4 and equation ( !!! ) by 5

192a + 160b = 36 __________ ( !!!!! )

180a + 160b = 35  _______________ ( !!!!!! )

Subtract ( !!!!!! ) from ( !!!!! )

We get,

→ a = 1/12

Substitute ' a '  = 1/12 in ( !!! )

we get ,

→ b = 1/8

Now 1/ ( x + y ) = 1/12

1/ ( x - y ) = 1/8

Hence,

x + y = 12 ________( 7 )

x - y = 8 _________ ( 8 )

Add ( 7 ) and ( 8 )

2x = 20

x = 10

Substitute  x = 10 in ( 7 ).

We get,

→ y = 2

Speed of the boat in still water

= x

= 10 km/h

speed of the stream

= y

= 2km/h

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