Question

please friends solve this also because its question 26 of class 10 board exam set 2

Answer 1

Hola there..

Speed of the motor boat = 18km/hr
Distance = 24 km

Let the speed of stream be 'x'.
So,
speed of boat in downstream = 18 + x
speed of boat in upstream = 18 - x

The boat takes 1 hr more to go to upstream than the down stream.

So,
the equation will be formed as,
$\frac{24}{18 - x} - \frac{24}{18 + x} = 1$
=>
$\frac{24(18 + x) - 24(18 - x)}{(18 + x)(18 - x)} = 1$
=>
$(24 \times 18) + 24x - (24 \times 18) + 24x = {18}^{2} - {x}^{2}$
=>
$48x = 324 - {x}^{2}$
=> x² + 48x - 324 = 0

=> x² + 54x - 6x - 324 = 0

=> x(x + 54) - 6(x + 54) = 0

=> (x + 54)(x - 6) = 0

=> x = -54 and 6

As, the speed of the stream cannot be negative so we will reject -54.

So, the speed of stream will be = 6 km/hr

I hope that this ans. helps you....:)