explain the answer

thanks for this explanation both of u 

Okay Lets do this:

Distance flown by the Airplane = 3500 Kilometers

Distance traveled by the train = 600 Kilometers

Lets make x the taken by the Airplane

Because of this, it would make sense that the time taken to travel 600 Kilometers is also x.

Now to find out the speed of the Airplane, the forumla is 

$${\frac{{\mathtt{3\,500}}}{{\mathtt{x}}}}$$

Now to find out the speed of the Train, the forumla is

$${\frac{{\mathtt{600}}}{{\mathtt{x}}}}$$

Now let us use what we already know.

$${\frac{{\mathtt{3\,500}}}{{\mathtt{X}}}} = {\mathtt{5}}{\mathtt{\,\times\,}}\left({\frac{{\mathtt{600}}}{{\mathtt{X}}}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{50}}$$

$${\frac{{\mathtt{3\,500}}}{{\mathtt{x}}}} = \left({\frac{{\mathtt{3\,000}}}{{\mathtt{x}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{50}}\right)$$

Now we need to eradicate the x

So we multiply x to both sides.

$${\mathtt{3\,500}} = {\mathtt{3\,000}}{\mathtt{\,\small\textbf+\,}}{\mathtt{50}}{\mathtt{\,\times\,}}{\mathtt{X}}$$

Now we need to use some basic algebra knowledge to solve this. Let us move x to one side and the numbers on the other. We will get

$${\mathtt{x}} = {\mathtt{10}}$$

Now, lets go back to what we know already know and substitute.

For the Plane:

$${\mathtt{SPEED}} = {\frac{{\mathtt{3\,500}}}{{\mathtt{X}}}}$$

$${\mathtt{SPEED}} = {\frac{{\mathtt{3\,500}}}{{\mathtt{10}}}}$$

$${\mathtt{SPEED}} = {\mathtt{350}}{KM}$$per hour

For the Train:

$${\mathtt{SPEED}} = {\frac{{\mathtt{600}}}{{\mathtt{X}}}}$$

$${\mathtt{SPEED}} = {\frac{{\mathtt{600}}}{{\mathtt{10}}}}$$

$${\mathtt{SPEED}} = {\mathtt{60}}{KM}$$ per hour.

There we go.

The Speed of the plane was 350KM per hour 

and the speed of the train was 60 Km per hour

Let the speed of the train be "x"

Then the speed of the plane is five times as fast plus 50km/hr = 5x + 50

Remember that Distance/Rate  = Time

And the time the train travels = Its Distance Traveled/Its rate  = 600/x

And the time the airplane travels = Its Distance Traveled/Its rate = 3500/(5x + 50)

But the times are equal....so

600/x = 3500/(5x + 50)

The easiest way to solve this is to just to take the cross products and set them equal, i.e.,

600(5x + 50) = 3500x       Expanding the left side, we have

3000x + 30000 = 3500x    Subtract 3000x from both sides

30000 = 500x                    Divide by 500 on both sides

60 = x   And that's the rate of the train in km/hr

And the plane's rate is 5(60) + 50 = 350km/hr

What good manners Rosala  

thank u melody