(6)

Let the speed of the stream be x km/h.

Therefore, the speed of the boat upstream = (18 – x) km/h and the speed of the boat downstream = (18 + x) km/h.

The time taken to go upstream = distance/speed = $\frac{24}{18+x}$

Similarly, the time taken to go downstream = $\frac{24}{18-x}$

According to the question, $\frac{24}{18-x}-\frac{24}{18+x}=1$

$\Rightarrow 24(18+x)-24(18-x)=(18-x)(18+x)\Rightarrow x^2+48x-324=0\Rightarrow x=6\text{ or }-54$

Since x is the speed of the stream, it cannot be negative. So, we ignore the root x = – 54. Therefore, x = 6 gives the speed of the stream as 6 km/h.

(44)

Let the average speed of the passenger train = x km/hour

And the average speed of the expresstrain = (x + 11) km/hour.

The time taken by the passenger train $=\frac{132}{x}$ hour

and the time taken by the express train $=\frac{132}{x+11}$ hour

According to the question, $\frac{132}{x+11}=\frac{132}{x}+1$

$\Rightarrow x^2+11x-1452=0$

$\Rightarrow (x-33)(x+44)=0\Rightarrow x=33, x=-44$

The speed cannot be negative, so the speed of the passenger train is 33 km/hour and the speed of the express train is 33 + 11 = 44 km/ hour.