Question

A motor boat whose speed js 18km/hr in still water takes 1 hr more to go 24km/hr upstream to return downlstream to same spot .Find the speed of the stream​

Answer 1

Answer:

let the speed of the stream be x km/hr

now,for upstream : speed =(18-x) km/hr

so, time taken

$= ( \frac{24}{18 - x} )hr$

now,for downstream : speed =(18+x) km/hr

so, time taken

$= ( \frac{24}{18 + x} )hr$

given that,

$\frac{24}{18 - x} = \frac{24}{18 + x} + 1$

$⟹ - 1 = \frac{24}{18 + x} - \frac{24}{18 - x}$

$⟹ - 1 = \frac{24(18 - x) - (18 + x)}{( {18}^{2}) - {x}^{2} }$

$⟹ - 1 = \frac{24( - 2x)}{324 - {x}^{2} }$

$⟹ - 324 + {x}^{2} = - 48x$

$⟹ {x}^{2} + 48x - 324 = 0$

$⟹ {x}^{2} + 54x - 6x - 324 = 0$

$⟹(x + 54)(x - 6) = 0$

x = -54 or x = 6

x = -54 km/hr (not possible)

x = -54 km/hr (not possible) Therefore speed of the stream = 6 km/hr