**Example 2:**

A train is passes a pole in 9 seconds completely and the same train passes the platform in 36 seconds completely. If the length of the platform is given to be 780 m, then find the length of the train.

**Solution:**

Let the length of the train be $x\ m$.

Distance covered by train in passing the platform = length of train + length of platform

$\Rightarrow$ Distance covered in passing platform = $x\ +\ 780$

Now according to question we have,

Speed of the train = $\frac{x}{9}$ m/s

Also, speed of the train = $\frac{(x + 780)}{36}$ m/s

Therefore, $\frac{x}{9}$ = $\frac{(x\ +\ 780)}{36}$

$\Rightarrow\ 36\ x\ =\ 9\ (x\ +\ 780)$

$\Rightarrow\ 4\ x\ =\ x\ +\ 780$

$\Rightarrow\ 3\ x\ =\ 780$

$\Rightarrow\ x\ =\ 260$

Therefore, the length of the train is 260 meters.

**Example 3:**

The speed of the boat in still water is 10 km/h. A man is taking four times the time to row up the boat in river as to row down the boat in river. Find the rate of the stream.

**Solution:**

Let the rate of stream be $x$ km/h

Then the speed of boat downstream = $(x\ +\ 10)$ km/h

And the speed of boat upstream = $(10\ –\ x)$ km/h

According to the question,

$x\ +\ 10\ =\ 4\ (10\ –\ x)$

$\Rightarrow\ x\ +\ 10\ =\ 40\ –\ 4x$

$\Rightarrow\ 5x\ =\ 30$

$\Rightarrow\ x\ =\ 6$

Therefore, the rate of the stream is 6 km/h.