Question

A motor boat can travel 30 km upstrem and 28km downstream in 7hr lt can travel 21 km upstream and return in 5hr find the speed of boat in still water and speed of the stream

Answer 1

LET THE SPEED OF MOTOR BOAT = X

AND THE SPEED OF STREAM = Y

THEN,

$\frac{30}{x - y} + \frac{28}{x + y} = 7 \\ \frac{30x + 30y + 28x - 28y}{ {x}^{2} - {y}^{2} } = 7 \\ \frac{58x + 2y}{7} = {x}^{2} - {y}^{2} \: ..... \: (1)$

IN 2ND CASE,

$\frac{21}{x - y} + \frac{21}{x + y} = 5 \\ \frac{21x + 21y + 21x - 21y}{ {x}^{2} - {y}^{2} } = 5 \\ \frac{42x}{5} = {x}^{2} - {y}^{2} \: ..... \: (2)$

NOW,

EQUALISING (1) & (2)

(58X+2Y)/7 = 42X/5

5(58X+2Y) = 7(42X)

290X+10Y = 294X

10Y = 4X

Y = (2/5)X ___ (3)

NOW, PUTTING THE VALUE OF Y IN EQUATION (1)

{30/(X-(2X/5)} + {28/(X+(2X/5)} = 7

30/(3X/5) + 28/(7X/5) = 7

30×5/3X + 28×5/7X = 7

50/X + 20/X = 7

70/X = 7

X = 10 KMPH

NOW,

PUTTING THE VALUE OF X IN EQUATION (3)

Y = (2/5)(10)

Y = 4 KMPH

SPEED OF MOTOR BOAT IN STILL WATER IS 10 KMPH

AND

SPEED OF STREAM IS 4 KMPH.

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