# a boat covers 32km upstream and 36km downstream in 7hours. also it covers 40km upstream and 48km downstream in 9hours. find the speed of the boat in still water and that of stream?

speed of still water=x

speed of stream=y

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

speed of boat down stream=(x+y)km/h

also,  time = distance/speed

in first casewhen the boat goes32km upstream ,let the time taken, in hour be t1. then

t1= 32/x-y

let the t2 be the timetaken by the boat to go down stream

t2=36/x+y

so eq is 32/x-y +36/x+y=7

in second case the eq is

40/x-y+48/x+y=9

subsitute 1x-y=u ,1/x+y=v

so we get 32u +36v=7........... eq  i

and 40u+48v=9

use elimination method  to solve eq i and eq ii then we get,

v=1/12

u=1/8

1/x-y=u  ,1/x-y=1/8

x-y =8 ..........eq 3

and x+y=12 eq 4

subtract both the eq we get

x=10

add both the eq we gt

y=2

so  ,speed of stillwater is10km /h and stream is 2km/h

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Thank uuu

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We can take the speed formula and can solve this ... Let 32 and 36 be distance and x+y and x-y be speed and time be 7 in this way also we can solve
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no its swrong

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Hi , 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.
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