Since Train B left at 2pm, it will pass Train A at 6pm. And if all you need to find is the point where the two trains meet, the easiest way is to add up the two speeds and find the ratio of each one to that sum, then multiply the distance by each of those fractions to find how far from each city the meeting point is. Gene G. It only takes a minute to sign up.
Here's a nice table to demonstrate the issue: 5AM 0 -- <-- Train #1 leaves the station at Town A, but hasn't traveled any miles yet, so it is 0 miles away from Town A. Incidentally, I wouldn't suggest trying to actually mention this at anything resembling a party, because someone might think you're making the joke I mentioned earlier and stop you halfway through, or else get confused when you use actual numbers and start to actually solve it instead of trying to call them nerds for trying to solve it themselves. A travels towards the train station B is at, while B travels towards the train station A is at. Our new equation for Train #2 is 455-d = 70x.
However, the equation d = 70x does NOT represent the distance Train #2 is from Town A, because it left from Town B. Update the question so it's on-topic for Mathematics Stack Exchange.
It can make up $60-40$ km deficit in an hour, So, it will require $80/20$ hours to meet train $A$. Train B starts with a lag of $2\cdot40$ km. When Train #2 begins to travel, Train #1 has already traveled 120 miles away from Town A (See table above.). If someone left at $t$ and you leave H hours later, why your time is $t - H$? If the trains are heading in different directions, and the question is "how far apart are they at 10:00", it's a more complex problem, but still algebra -- now two-dimensional, and possibly parametric. But the second train (B) departed at $2$ P.M. That's how far that train will go before they meet. If they could go a full hour they would go 100 miles, so they would go a total of 50 miles in half an hour. Also, the time zone difference shouldn't matter. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. strangers build memorials to the wreckage; they leave crosses by the tracks, silk flowers that the wind drags away. If that didn't make sense let me know what you don't get. That means it will have covered about two thirds of the total distance at the time the trains meet. t&=4hours how far has bird flown when two trains cross each other, Checking target legality (esp for removal). Not $t + H$?
If that is the case, then it has a bad answer because in the time the 2 trains travelled, they would not have crossed the timezone. But since that joke isn't really worth explaining, I'll focus on the real version of the question, which really can be solved, and requires that you have actual some actual numbers involved, specifically for three things: the distance between the cities The speed of each of the two trains (they have to be different, or else the problem is so simple it's not a real problem). Or in terms of train B, it traveled a total of yz/(x+y) miles west, so the answer is also yz/(x+y) miles west of train B's starting position.
In other words, $S/60 = S/40 -2$, so $S=240$ (miles).
the distance between Town A and Town B is 455 miles. answered 08/13/13, Retired Electrical Engineer - ACT Prep, Free Official Practice Tests.
It asks how much time until they meet. You want to make sure you get that before going on.
Train #1 equation: d = 60x + 120 ; Train #2 equation: 455 - d = 70x. As train $B$ travels at $60$ mph it needs $4$ hours to overtake train $A$. Two hours later Train B leaves the same station, also for Chicago, traveling 60mph. So the question becomes, how long will it take before the trains travel a combined total of 300 miles? Clearing up property and field confusion in C#. Why does 60 Hz mean 60 refreshes and not 120? Math contest problem about 2 trains leaving the same station at different times [closed], Hot Meta Posts: Allow for removal by moderators, and thoughts about future…, Goodbye, Prettify. Seeing as how I chose for Town A to be at mile #0, the equation d = 60x also tells us how far Train #1 is from Town A.
When and where do they collide?
The question, as posted, asks how long it takes for Train B to pass Train A, so the answer is 4 hours, not 4pm or 6pm. What are the closure properties of LL(k) languages?
Let me know if you need more help or if you have any questions about the explanation thus far. Train A went a grand total of 60×3=180 miles. I thought about it some more and I believe it might have something to do with the time difference between the 2 cities? Press J to jump to the feed. Try it! I have a math problem from a math contest I will be taking soon that I simply cannot understand how they got their answer. \\ I know that when the two trains meets the sum of their distances travelled will be equal to the total sum, here is what I know so far And you know that the trains will meet in the amount of time it takes for the combined distance traveled by both of them to equal 150 miles. The time when the two trains will meet is going to be the solution to the following equation (the intersection of two straight lines) where $t\ge0$ and $t=0$ corresponds to $12:00$ PM (noon): $$ In general, if train A and train B are z miles away, and train A is going x mph and train B is going y mph, then in 1 hour they will travel a total of x+y miles. The trick with word problems is to pick them apart to see what you know, then build equations that you can solve. You could also phrase it in terms of train B: it traveled 120 miles total, so they crash 120 miles west of train B's starting position. Let's calculate how far it goes in those two hours: d = rt = 2 hrs * 60 mi/hr = 120 miThe time is now 7:00 and the trains are 455 - 120 = 335 mi apart. That's 2 hours with a remainder of 0.57690.5769 * 60 minutes = 34.615 minutes0.615 * 60 seconds = 37 seconds, The time of collision will thus be the sum of 2 hrs + 2.5769 hrs added to the 5:00 starting time.Tc = 5:00 + 4.5769 = 5:00 + 4:00 + 0:34 + 0:00:37 = 9:34:37. Since Train B left at 2pm, it will pass Train A at 6pm. Equivalently (and possibly easier to do in your head), divide the speed of one train by the sum of the speeds (again, assuming they're heading towards each other).
Is there a Google Maps like app that shows directions and other people's progress along the same route?
rev 2020.9.30.37704, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. Can anyone dumb it down for me further?
in another, the trains crash into one another.
Lots of good answers here. Train A leaves at time $t_{A0} = 0$ traveling at $40$ mph. Hello highlight.js! The first, which I expect is somewhat more common, is really just a joke, with a punchline vaguely along the lines of "who cares, you lousy nerd".
Several good answers already but let me add one more. 80+40t&=60t Times are equal so d1/s1 = d2/s2 for each train.
Thus, we can solve the equation for time: 260/130 = 2. The best way that I've found to approach this type of question is by drawing a picture. Divide the distance between their starting points by the closing speed, to get how long it'll take them to meet. Swapping out our Syntax Highlighter.
We can reorganize this equation to state Distance/Rate = Time.
The sum of both distances is the total distance. Danielasdf B. It's usually posed as something like 'One train leaves San Fran travelling X mph. From there, you can easily calculate the location.
So you know they will meet at the geographic location that is two thirds of the trip away from that train's destination, but maybe a tiny bit short due to the way we approximated.
The math still works because 50/100=1/2. This is the best (simplest) explanation I've seen, but still explains like i'm in high school.
So they will travel a total of z miles in z/(x+y) hours.
7AM 120 455 <-- Train #2 leaves the station at Town B, but hasn't traveled any miles yet, so it is 455 miles away from Town A. Instead, if we write the left side of the equation as 455-d, we are able to find out how far Train #2 is from Town A. It takes some practice. At $4$:$00$, train $A$ will have gone $4\times 40=160$ miles and train $B$ will have gone $2\times 60=120$ miles so that seems incorrect. I believe Chicago is 2 hours ahead of San Francisco so it makes the answer 4 P.M. instead of 6 P.M. however, I'm not sure. \\ When and where do they meet? Sometimes, a problem will even ask where they would meet. So, the combined speed of both trains is 170 mph, which means that the can cover 150 miles in 150/170 = 0.88 hours. Symplectic structure on the square of a 3-manifold, "Roll Over" in the Song Roll Over Beethoven.
... you could calculate how far each one went and find the exact location where they meet. Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away.
Explain Like I'm Five is the best forum and archive on the internet for layperson-friendly explanations. Why do people say the Pakistani government has failed because the army is interfering with politics? They both went for 3 hours. So they crash in 300/100=3 hours. If a stopwatch was started in one traincar, the time zone difference wouldn't change the elapsed time. And because I conveniently chose a multiple of 9 for the distance, that's 36 miles from city 1 and 45 miles from city 2. Another train leaves point B at 7 am and reaches point A at 10:30 am.When will the two trains meet ? So they crash 180 miles east of train A's starting point.
Here's mine: [Train #1] --> *Boom* <-- [Train #2], (Town A = Mile #0) (Town B = Mile #455). A train leaves point A at 5 am and reaches point B at 9 am. Must one say "queen check" before capturing a queen? Here's another spin on it: If the trains are heading toward each other on the same line, and the question is "when do they meet", it's a simple algebra problem -- it's one-dimensional, and requires solving one equation. As you can tell by now, explaining this sort of thing is much easier with an example: Distance: 81 miles Train 1 speed: 20 miles/hour Train 2 speed: 25 miles/hour.
Both equations use the same meaning for d and for x, so your next step would be to combine them into one equation and solve for x (which should be the only variable left in your combined equation).