Question

A boat whose speed is 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream is ___ km/hr.

Answer 1

Answer:

The speed of the boat will be 15 + v km/hr downstream and 15 - v km/hr upstream. Time taken by the boat in travelling 30 km downstream and back is (30/(15 + v) + 30/(15 - v)), which is 4.5 hrs. Solving this equation we get v = 5. Therefore the speed of the stream is 5 km/hr.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

speed of the boat = 15kmph

let the speed of stream be x

$for \: upstrem$

For upstream ,the speed of stream opposes the speed of boat

so,

$speed \: = \: 15 - x$

$w \: know \: that \: speed \: = \frac{distnance}{time}$

$15 - x = \frac{30}{t}$

$t = \frac{30}{15 - x}$

$for \: downstrem$

For downstream,the speed of stream supports the speed of the man

$speed = 15 + x$

$speed = \frac{distance}{time}$

$15 + x = \frac{30}{t}$

$t = \frac{30}{15 + x}$

But given that it returns in 4hours 30 minutes

= 4 1/2 hours

So t + t = 4 1/2

t+t = 9/2

$\frac{30}{15 - x} + \frac{30}{15 + x} = \frac{9}{2}$

$\frac{30(15 + x) - 30(15 - x)}{(15 + x)(15 - x)} = \frac{9}{2}$

$\frac{450 + 30x - 450 + 30x}{ 225 - {x}^{2} } = \frac{9}{2}$

$\frac{60x}{225 - {x}^{2} } = \frac{9}{2}$

$120x = 2025 - 9 {x}^{2}$

${9x}^{2} + 120x - 2025 = 0$

Taking three as the common factor

$3( {3x}^{2} + 40x - 675) = 0$

${3x}^{2} + 40x - 675 = 0$

${3x}^{2} + 75x - 25 x - 675 = 0$

$3x(x + 25) - 25(x + 25) = 0$

$(x + 25)(3x - 25) = 0$

$3x - 25 = 0$

$3x = 25$

$x = \frac{25}{3}$

$x = 8.33$

Therefore ,rate 0f stream is 8.33 km/hr

HOPE IT HELPS.............