two trains are headed right for eachother they are 180 miles apart. train A is going 50mph, train B is going 40 mph train A starts at point A. when will they collide and where will they collide in reference to point A?

I dont even know where to start on this problem, it just is confusing me...please help !!! thnaks

JChev06

They will collide in 2 hours, they will be 100 miles from point A.

Just multiply each trains speed by 2 (that equals 180 miles) and that's how you get the answer.

Capuchin

write an equation for x (distance apart)

x = 180 - (50+40)t

this gives you the distance they are apart, solve for x = 0 to find how many hours (t) it takes for them to collide.

Then you can use speed = distance/time to find the distance train A has travelled from point A until they collide (at time t)

If you need further help, please ask.

Capuchin

JChev06, although your answer is correct, please read This Announcement for the site's policy on helping people with homework

JChev06

Sorry, I was not aware of that. Won't happen again.

CaptainForest

JChev06,

That is not an official policy that you have to abide by.

I don't always.

If you wish to help people with their homework, that is your decision.

Sometimes I do, but other times, when they don’t even post how they attempted it, I don’t bother to.

Capuchin

Sure, you don't need to bother, but if you do, stating how to get the answer is much more useful than the answer itself

newb

OK, I'm going to show you a way to do it that will make all of these problems look the same. You're teacher will probably make a chart, unfortunately, to do this problem. My method is similar to Capuchin's method. You need to know to do two things to solve these types of problems: 1) convert what they give you into a statement about lengths of line segments; and 2) know that distance = rate times time (d = rt). That's it! Let's do 1) first.

Da Db
1) A_______________x__________B

<---------------180---------------->

The picture show that line segment 180 = Da + Db (Where Da is distance that a travels before the collision and Db is the distance that b travels before the collision).

Now replace Da with RaTa and Db with RbTb. So the above equation becomes 180 = RaTa + RbTb. Now plug in what you know, namely Ra = 50 and Rb = 40. The equation becomes 180 = 50Ta + 40Tb. Notice that train A leaves point A at the exact same time that train B leaves point B. The key point is that when they collide they've been on the tracks the same amount of time since they left their respective points A and B. So we can write Ta = Tb = T and the equation becomes 180 = 50T + 40T. Now solve for T. Notice that if you delete all the words, it takes about 4 lines to solve the problem!

Phil

Capuchin

Hi newb, thanks for explaining how I got my equation

Why do you use "rate" instead of "speed"?
Speed is more specific, as rate can be interpreted as many many things.

newb

Hi Capuchin,

This IS a rate. That is to say it has both magnitude (speed) and most certainly direction. That's why we refer to these as Distance/Rate/Time problems instead of Distance/Speed/Time problems and we write d = rt, not d = st.

Phil