How do you solve train problems, ---- make it as simple as possible!!!

How do you solve train problems, and please make it as simple as possible!!!?

For example, Train A leaves a station at 40 miles per hour. Six hours later train B leaves the same station traveling in the same direction at 60 miles per hour. How long does it take for train B to catch up to train A? Answer choice [A] 14 hr [B] 13 hr [C] 16 hr [D] 12 hr

Answer

Algebra (and that's all a train problem is) is always just writing any sentance in a really quick way so you can figure out was going on.
So for your example problem train A is traveling 40mph
and train B 60mph the only other factor is train A leaves 6 hours before train B. We are looking for x (this can be any letter) which is the time when they are together.
At that time Train A will have been traveling 6 more hours the train B (that's true at any time). So if TrainB travels for x hours TrainA travels for x+6 hours.
The distance traveled when they cross will be thier traveling time multiplied by thier speed.
When they cross:
trainA will have traveled x+6 hours at 40mph
trainB will have traveled x hours at 60mph
but here's the trick thier distance travelled will be the same.
40(x+6)=60x
that's the equation we needed it links the twobits of info and has only 1 unknown.
Here's the option now you can solve
eg
40(x+6)=60x
(x+6)=1.5x (divide both sides by 40)
x+6=1.5x
6=0.5x (minus x from both sides)
12=x (double both sides)
so that means train b will over take train A 12 hours after it leaves the station.

The othe choice with multiple choice is when you 40(x+6)=60x the equation (40(x+6)=60x) just enter 13, 14, 16 and 12 and see which one holds true.

You will however need to set up the equation either way.

Good luck!