Question

Hey !!

A Motor Boat can travel 30km upstream and 28 km downstream on 7 hrs.
It can travel 21 km Upstream a s 40km downstream in 5hrs. Find speed of Stream And Boat...

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#Surya...

Answer 1

Heya !!

Here's your answer.. ⬇⬇

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Let speed of boat in still water be x km/hr and speed of stream be y km/hr.

We know, Speed = Distance/Time

Time = Distance/Speed

In 1st case, when boat travels 30km upstream, let time taken in hours be t1.

t1 = 30/( x-y )

let t2 be the time in hours taken by boat to go 28 km downstream.

t2 = 28/( x+y )

Total time taken is t1 + t2 is 7hrs.

30/( x-y ) + 28/( x+y ) = 7. ---( 1 )

In 2nd case, in 5hrs it can go 21km upstream and 40km downstream.

21/( x-y ) + 40/( x+y ) = 5 ---(2)

Let 1/( x-y ) = a and
1/( x+y ) = b

Now, new eq. will be..,

30a + 28b - 7 = 0 ----( 3 )
21a + 40b - 5 = 0 ----( 4 )

Solve by cross multiplication..,

a1 = 30, b2 = 28, c2 = ( -7 )
a2 = 21, b2 = 40, c2 = ( -5 )

$\frac{a}{b1c2 - c1b2} = \frac{b}{c1a2 - c2a1} = \frac{1}{a1b2 - a2 b1} \\ \\ \frac{a}{28( - 5) - ( - 7)(40)} = \frac{b}{( - 7)(21) - ( - 5)(30)} = \frac{1}{30(40) - 21(28)} \\ \\ \frac{a}{ - 140 + 280} = \frac{b}{ - 147 + 150} = \frac{1}{1200 - 588} \\ \\ \frac{a}{140} = \frac{b}{3} = \frac{1}{612} \\ \\ a = \frac{140}{612} \: \: \: b = \frac{3}{612} \\ \\ \frac{1}{x - y} = a = \frac{35}{153} \: \: \\ \\ \frac{1}{x + y} = b = \frac{1}{204} \\ \\ x - y = \frac{153}{35} \: \: ...(5) \\ \\ x + y = 204 \: \: \: \: ..(6) \\ \\ 35x - 35y = 153 \\ \\ multiply \: \: eq.(6) \: \: by \: \: 35 \\ \\ 35x + 35y = 7140 \\ \\ add \: \: both \: \: eq. \\ \\ we \: \: get \: \: \\ \\ 70x = 7293 \\ \\ x = 104.18 \\ \\ x + y = 204 \\ \\ y = 204 - 104.18 \\ \\ y = 99.82$

x = 104.18
y = 99.82

Speed of boat ( x ) = 104.18 km/hr.
Speed of stream ( y ) = 99.82 km/hr.

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Hope it helps..

Thanks :))