Question

EXAMPLE 4 A boat covers 32 km upstream and 36 km downstream in 7 hours. Also, it covers 40 km
upstreamikud 48 km downstream in 9 hours. Find the speed of the boat in still water and that of the
stream.
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Answer 1

Let the speed of the boat in still water = x kmph

Speed of the stream = y kmph

i ) relative speed of the boat in downstream

= ( x + y ) kmph

Distance travelled = d1 = 36

Time = t1 hr

t1 = d1 / s1

t1 = 36/ ( x + y )

ii) relative speed of the boat in upstream = ( x - y ) kmph

Distancw = d2 = 32 km

Time = t2

t2 = 32/ ( x - y )

Therefore ,

Total time = 7 hr

t1 + t2 = 7hr

36 / ( x + y ) + 32/ ( x - y ) = 7 ----( 1 )

iii) second time ,

Relativespeed of the boat in downstream = ( x + y ) kmph

d3 = 48 km

Time = t3

t3 = 48/ ( x + y )

iv ) in upstream

Relative speed of the boat = ( x - y )kmph

time = t4 hr

d4 = 40km

t4 = 40/ ( x - y )

Total time = 9 hr

48 / ( x + y ) + 40/ ( x - y ) = 9 ---( 2 )

Let 1 / ( x + y ) = a ,

1 / ( x - y ) = b

Then rewrite ( 1 ) and ( 2 ) we get

36 a + 32 b = 7 -----( 3 )

48a + 40b = 9 ------( 4 )

Multiply ( 4 ) with 4 and equation ( 3 ) with 5 and

192a + 160b = 36 ---( 5 )

180a + 160b = 35 -----( 6 )

Subtract ( 6 ) from ( 5 )

we get

a = 1/ 12

put a = 1/ 12 in ( 3 )

we get ,

b = 1/ 8

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

1/ ( x - y ) = 1/ 8

Therefore ,

x + y = 12 ----( 7 )

x - y = 8 ----- ( 8 )

add ( 7 ) and ( 8 )

2x = 20

x = 10

put x = 10 in ( 7 ) we get

y = 2

Speed of the boat in still water = x = 10 kmph

speed of the stream = y = 2kmph

I hope this helps you.