Question

A motorboat, whose speed in 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 (in km/hr) is: indiabix

Answer 1

solution:

let the speed of the stream be x km/hr

then,\\

speed downstream= (15+x)km/hr

speed upstream = (15-x)km/hr

\frac{30}{(15+x)}+\frac{3}{(15-x)}=4\frac{1}{2}\\

\frac{900}{225-x^2}=\frac{9}{2}\\

9x^2=225\\

x^2=225\\

x^2=25\\

x=5km/hr

Answer 2

The speed of the stream is 5 km/hr.

Explanation:

Let the speed of the stream is v.

The speed downstream is given as = (u + v) km/hr

and speed upstream = (u - v) km/hr.

Here u is the speed of the boat in still water.

Given u = 15 km/hr and  d = 30 km and total time, t = 4 hr 30 min = 4.5 hr.

So, the time taken to travel downstream

 $t_1=\frac{30}{15+v}$                   (using time, speed and distance relation.)

and the time taken to travel upstream,

$t_2=\frac{30}{15-v}$

Therefore, total time

$t=t_1+t_2$

substitute the values, we get

$4.5hr=\frac{30km}{15km/hr+v}+\frac{30km}{15km/hr-v}$

$\frac{9}{2}hr=\frac{900}{225-v^2}$

v = 5 km/hr

Thus, the speed of the stream is 5 km/hr.

#Learn More: speed, time and distance

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