# Math Help - When will the two trains meet.

1. ## When will the two trains meet.

Towns A and B are 400 miles apart . If train A leaves in direction of B at 50 mph , how long will it take before that train meets another train going from B to A at the speed of 30 mph ?
The ans is 5 hours

I calculated the time duration of first train is 13.3 hr and the second is 8hr.However i cant figure out when they will meet.

2. ## Re: When will the two trains meet.

you can figure it like this

the distance of the first train could be $d_1(n)=50n$

the distance of the first train could be $d_2(n)=30n$.

So, when will they meet?

They will meet if the sum of the distances is 400, that is
$50n+30n=400$

solving this equation to get that $n=5.$

3. ## Re: When will the two trains meet.

The question doesn't indicate that the two trains leave at the same time. Oh well, I'll assume they do.

Another way to do it is: Relative to train B, train A is moving 80 mph. They begin 400 miles apart, so it will take five hours for the two trains to meet.

4. ## Re: When will the two trains meet.

Hello, MikeNoob!

Towns A and B are 400 miles apart. .If a train at A leaves in he direction of B at 50 mph
and a train at B leave in the direction of A at 30 mph, how long will take for the trains to meet?

I calculated the time duration of first train is 13.3 hr and the second is 8 hr. .These are reversed.
However i can't figure out when they will meet. .Of course you can't!

The train at A moves east at 50 mph.
The train at B moves west at 30 mph.
Their combined speed is 80 mph.

As richard1234 suggests, it is as if the train at B stays at B
. . and the train at A approaches it at 80 mph.

To cover the 400 miles, the train at A will take 5 hours.

5. ## Re: When will the two trains meet.

Originally Posted by MikeNoob
The ans is 5 hours

I calculated the time duration of first train is 13.3 hr
Then you did something seriously wrong. At 50 mph, the first train will have traveled 50(13.3)= 665 miles, greater than the 400 miles the two trains were apart to begin with.

and the second is 8hr.However i cant figure out when they will meet.