QUESTION:- A boat goes 30km in upstream and 44 km in downstream in 10hrs. In 13hrs ,it can go 40km upstream and 55 km downstream. Determine the speed of the stream and that of the boat in still water respectively

Time taken to cover 44 km downstream⇒x+y44

According to the first condition,

⇒x−y30=x+y44=10

Time taken to cover 40 km upstream ⇒x−y40

Time taken to cover 55 km downstream ⇒x+y55

According to the second condition,

⇒x−y40=x+y55=13

Let x−y1=uandx+y1=v

⇒30u+44v=10.....eq1⇒40u+55v=13.....eq2

Multiplying   eq1   by   3  and  eq2  by  5  and  subtract  both

⇒(150u+220v=50)−(160u+220v=52)

⇒−10u=−2⇒u=51

put  u=51 in eq1

⇒30×51+44v=10⇒44v=4⇒v=41

⇒u=x−y1=51⇒x−y=5...eq3

⇒v=x+y1=111⇒x+y=11...eq4

Subtracting eq3 and eq4, we get

⇒x=8

Put x=8 in eq3

⇒y=3

Hence, the speed of the boat in still water=8km\hr

The speed of stream=3km\hr

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