Question

a motor boat heads upstream a distance of 24km in a river whose current is running at 3km/h the trip up and back take 6hours. assuming that the motor boat maintained a constant speed ? what was its speed in still water?​

Answer 1

Answer:

9 Km/hr

Step-by-step explanation:

Let the speed in still water be X Km/hr

It implies that

• Speed upstream = X-3
• Speed downstream = X+3

$time \: upsteam = \frac{24}{x - 3} \: \: \: \: \: \: \: \: \: \: (1)$

$time \: downstream \: = \frac{24}{x + 3} \: \: \: \: \: (2)$

$total \: time = (1) + (2) = 6$

Therefore

$\frac{24}{x - 3} + \frac{24}{x + 3} = 6$

$\frac{24( x + 3) + 24(x - 3)}{ {x}^{2} - 9 } = 6$

$48x = 6( {x}^{2} - 9)$

${x}^{2} - 8x - 9 = 0$

$(x - 9) \times (x + 1) = 0$

Solving we get

$x = 9 \: and \: x = - 1$

Discarding x=-1 as negative speed is not possible we get speed in still water=9 Km/hr