Question

A motorboat whose speed is $18$ km/h in still water takes $1$ hour more to go $24$ km upstream than to return downstream to the same spot. Find the speed of the stream. $\left[4\right]$

Answer 1

Let the speed of the stream be represented by $x$. Therefore, the speed o the motorboat upstream is $(18-x)$ km/h and the speed of the motorboat downstrean is $(18+x)$ km/h. $\left[1Mark\right]$

Time taken by the boat to go upstream $=\frac{Distace}{Velocity}=\frac{24}{18-x}$

Similarly, the time taken by the boat to go downstream $\frac{24}{18+x}$

From the condition given here, we have: $\frac{24}{18-x}-\frac{24}{18+x}=1$ $\left[1Mark\right]$

$24x+24x=324-x^2$
$x^2+48x-324=0$
$x^2+54x-6x-324=0$
$(x-6)(x+54)=0$
$x=6,-54$
As speed can’t be negative
Speed of stream $=6$ km/hr $\left[2Marks\right]$