Question

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Q.24. A boat goes 30km upstream and 44km downstream in 10 hours. In 13hours, it can go
40km upstream and 55km downstream. Determine the speed of the stream and that of
the boat in still water.

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Answer 1

let the speed of boat still In water be x km/hr and the speed of the stream be y km/hr

then,

speed of boat upstream=x-y

speed of boat downstream=x+y

30/x-y +44/x+y=10

40/x-y +55/x+y=13

let x-y be u and x+y be v

by elimination method

30u+44v=10 ×4

40u+55v=13 ×3

120u+176v=40

120u+165v=39

11v=1

v=1/11

u=-1/30

x+y=-30

x-y=11

x=41/2=20.5

y=9.5

so speed of boat still In water is 20.5 km/hr

and speed of stream =9.5km/hr