A train X starts at A at 4 p.m. and reaches B at 5 p.m., while another train Y starts from B at 4 p.m. and reaches A at 5.30 p.m. At what time will the two trains cross?

All right, so let's assume that the distance between A and B here, A, B, will denote that distance as D. So train X starts from A and goes to B between 4 p.m. and 5 p.m., which means that it takes one hour for the train to travel from A to B.

And we can denote the speed of that train being that it travels D kilometers per hour for train X.

Train Y starts from B and goes to A, and it goes from 4 p.m. to 5.30 p.m., which means that it takes one and a half hours for train B to travel.

And for us to calculate the speed of that train, this is assuming that the trains are traveling at the constant speed, by the way.

So to calculate the speed of train Y, we need to do distance divided by the time it takes, which is one and a half hours, which is the same as saying three divided by two.

which you can also write as two divided by three times D kilometers per hour.

So now that we have the speed the trains are traveling in, we need to calculate the time it takes the trains to travel to a certain distance.

So let's call T time, okay?

So in order to calculate how far a train travels in time, we can do the first train, train X, and that's quite simple because it's just traveling in a ratio of one to one.

So it's traveling in this distance times T,

That's how far the train X will travel in time.

The other train, it's a similar thing, so it's the new value here, 2 divided by 3D times T is how many kilometers train Y will travel at a certain time.

So one property of this problem too is that when the two trains cross, they will both have traveled the sum of the total distance.

And we can write that as equation that is dt plus two divided by three dt equals d.

So now that we have the equation, we can solve for t to figure out when they meet.

So dt plus 2 divided by 3 dt equals d. You can simplify this as writing it as 5 over 3 dt equals d. To get rid of the 5 divided by 3 d, we divide by that on both sides, which gives us t equals d divided by 5 divided by 3.

When you have the same numerator and denominator you can get rid of that.

Which gives us t equals 1 divided by 5 divided by 3.

And this is the same as saying t equals 3 divided by 5.

So now we have t and 3 divided by 5 is 0.6.

equals 0.6.

So this is how many hours it takes.

It takes 0.6 hours for the two trains to meet.

And 0.6, if you wanna get this in minutes, you do 0.6 times 60, which is 36.

36 minutes.

So the two trains will meet, they started at 4 p.m.

So the trains will meet at 4.36 p.m.