Question

Aerosmith cover a distance of 50 kilometre downstream in one and half hour it covers this distance upstream in 2 hours the speed of the race boat in still water is 35 kilometre per hour find the speed of the stream

Answer 1

LET THE SPEED OF THE STREAM BE
x km/ hr.

WHEN RACE BOAT TRAVELS DOWNSTREAM:
speed=35+x

when race boat travels upstream : speed =35-x

$we \: know \: that \\ time \: = \frac{distance}{speed}$

BY THE GIVEN CONDITION,
$\frac{60}{35 + x} + \frac{60}{35 - x} = 1 \frac{1}{2} + 2$

$60(\frac{1}{35 + x} + \frac{1}{35 - x} ) = \frac{3}{2} + 2$

$60( \frac{35 - x + 35 + x}{(35 + x)(35 - x)} ) = \frac{3 + 4}{2}$

$60( \frac{35 + 35}{ {35}^{2} - {x}^{2} } ) = \frac{7}{2}$

$( \frac{70}{1225 - {x}^{2} } ) = \frac{7}{2} \times \frac{1}{60}$

$\frac{70}{1225 - {x}^{2} } = \frac{7}{120}$

$7(1225 - {x) }^{2} = 120 \times 70$

$8575 - 7 {x}^{2} = 8400$

$8575 - 8400 = 7 {x}^{2}$

$175 = 7 {x}^{2}$

$\frac{175}{7} = {x}^{2}$

$25 = {x}^{2}$

$i.e \: \: {x}^{2} = 25$
$by \: taking \: square \: root \:$

$x = 5$
$therefore \: we \: get$

$the \: speed \: of \: the \: stream \: is \\ \:5km \: per \: hour$

$hope \: this \: helps$