I need to put this word problem into a system of equations.?

Question

A train travels 150km in the same time that a plane covers 400km. If the speed of the plane is 20km per hr less than 3 times the speed of the train, find both speeds.

I don't need anyone to actually solve for x and y. I just need to know how to put this into a system of equation. Thanks

Answer 1

3x-20=y
150y=400x

where x is the speed of the train and y is the plane's speed

Answer 2

Let's call the speed of the train=x and the speed of the plane=y. We can't just put these 2 speeds (or rates) on separate sides of an equal sign since a plane moves faster, so let's handicap the speed of the train to make their comparisons balanced:

3x-20 = y
rate of train = x
rate of plane = 3x - 20
(by phrasing both in terms of rate of train, we reduce the # of variables, thus simplifying the equation)

Then set representatives for their times as equal (as stated). Following that, I'm going to replace the times in terms of distance and speed (or rate). Since Distance = Rate * Time, then Time = distance / Rate:

Time of train = Time of plane
Distance/Rate of train = Distance/Rate of plane
150/x = 400/(3x-20)

you can pretty this up some with a little cross multiplication:
150(3x-20) = 400x

and etc.....