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A Boat Goes 30 Km Upstream and 44 Km Downstream in 10 Hours. in 13 Hours, It Can Go 40 Km Upstream and 55 Km Downstream. Determine the Speed of the Stream and that of the Boat in Still Water. - Mathematics

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Sum

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

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Solution

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

And stream y km/h 

According to question,

`30/("x - y") + 44/("x + y") = 10`

And 

`40/("x - y") + 55/("x + y") = 13`

Let `1/"x - y" = "u" and 1/"x + y" = "v"`

30u + 44v = 10 ...(i)
40u + 55v = 13 ..(ii)

On solving equation (i) and (ii) we get,

u = `1/5 => "x - y "= 5`        ........(iii)

v = `1/11 => "x - y "= 11`        ........(iv)

On solving equation (iii) and (iv) we get,

x = 8 km/h

y = 3km/h

Concept: Application of Quadratic Equation
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