Two trains and straight line movement

[mmoadi]

Homework Statement

The train travels from place A to place B for one hour. Forty minutes after the departure, first train meets with second train, which departed from place B ten minutes after first train, and it’s traveling with an average speed of 40 km / h.

Homework Equations

What is the distance between points A and B? Assuming that the movement of trains at all times can be described as consistent evenly.

The Attempt at a Solution

I really need some help because I don not know where to start.

 

[tiny-tim]

Welcome to PF!

Hi mmoadi! Welcome to PF!

Start by calling the distance x km … then the speed of the first train is x km/hour.

Show us what you get. ​

 

[mmoadi]

I know that the it takes for the first train to travel the distance between A and B in 1 hour.
Does this mean that the v1 (velocity of the first train) is v1= d/t which gives us that the v1 = d after I plug in the time which is 1 hour?
I also know that the two trains meet after the first train has traveled for 40 min (t1) and that the average speed of the second train is 40 km/h (v2).
So, in my opinion the whole distance is s= v1t1 + v2t2. Am I right?
So how do I continue?

 

[mmoadi]

I did some more thinking.
So, I know that the speed(v1) of the first train is v1=d. And the two trains meet after 40 min(2/3h) and the second train leaves 10 min after the first train, so does this mean that it travels for 40min-10min=30 min (1/2h) before it meets the first train. If I am right than it comes to:
s= v1t1 + v2t2 = d(2/3h) + 40km/h(1/2h)= 2/3d + 20km
d - 2/3d = 20 km
d(1-2/3) = 20 km
1/3d=20 km
d= 60 km

Is my solution right?

 

[tiny-tim]

Woohoo! ​

Yes, that's exactly the way to do it …

and we can always check the answer (which I did ) by putting 60 back into the original question, and confirming that it works!