If the trains are heading in different directions, and the question is "when are they closest together", it's a calculus problem, as are most min/max problems. Train A traveled xz/(x+y) miles total, so the answer is xz/(x+y) miles east of train A's starting position. To check, their distances added together should be 455 when you're finished. my grandmother whispers the gory details of it all over phone lines to her church friend, and it’s all too much to speak about too loudly. The question wants you to figure out when the trains are at the exact same point on the tracks (in my picture above, when the trains go *Boom* :) ). ... you could calculate how far each one went and find the exact location where they meet. 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. how far has bird flown when two trains cross each other, Checking target legality (esp for removal). Thus, we can solve the equation for time: 260/130 = 2.
80+40t&=60t t=6\ P.M. Here's mine: [Train #1] --> *Boom* <-- [Train #2], (Town A = Mile #0) (Town B = Mile #455). Word problems can be tough. 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.
So at that point we have a distance and two speeds. Since Train B left at 2pm, it will pass Train A at 6pm. So, it takes 4 hours for train B to close the 80 miles between the two trains (80 miles / 20mph). 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. So, it takes 4 hours for train B to close the 80 miles between the two trains (80 miles / 20mph).
Now if you feel like it you can confirm this by finding the time it takes for the trains to meet, by dividing each of those distances by each of the speeds, which should give the same thing: 36 mi / 20 mph = 1.8 hours 45 mi / 25 mph = 1.8 hours And now because the time is the same and the two distances add up to the total distance between the cities (45+36 = 81), you can tell you didn't make a mistake somewhere. It can make up $60-40$ km deficit in an hour, So, it will require $80/20$ hours to meet train $A$. A link to the app was sent to your phone. In the two hours where only Train A is traveling, it goes a total of 80 miles (40mph x 2 hours). From there, you can easily calculate the location. Likewise, Train #2 is traveling at 70 miles per hour, so the distance this train travels can be represented by the equation d = 70x (the variables mean the same thing). 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). Now, the trains don't leave their stations at exactly the same time, so we can't just replace the d in Train #2's equation with 60x. Want to improve this question? Does the airport security/ TSA know how to open zipperless hardshell luggage? Then multiply the speed of one train by that time, to find out how far from that train's starting point they'll be when they meet. A travels at 70 mph and B travels at 60 mph. When and where do they meet?
Not $t + H$? How long until Train B overtakes Train A? answered 08/13/13, Retired Electrical Engineer - ACT Prep, Free Official Practice Tests. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. \end{align}$$. After 1 hour, train A went 60 miles and train B went 40 miles. We can reorganize this equation to state Distance/Rate = Time. Incidentally, I wouldn't suggest trying to actually mention this at anything resembling a party, because someone might think you're making the joke I mentioned earlier and stop you halfway through, or else get confused when you use actual numbers and start to actually solve it instead of trying to call them nerds for trying to solve it themselves.
Because I've seen the question posed hypothetically a hundred times, but never seen it answered. Clearing up property and field confusion in C#.
answered 08/13/13. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. For example, if one train is going 100 mph and the other is traveling 70 mph, then the total speed is 170. But for the first case, using the combined speed to estimate how fast they are closing on each other is the Best Approach, and something you can nearly always do in your head. Two trains leaving the station at different times... Two trains are driving toward one another. Train A, traveling 70 miles per hour (mph), leaves Westford heading toward Eastford, 260 miles away. That's how far that train will go before they meet. The time when the two trains will meet is going to be the solution to the following equation (the intersection of two straight lines) where $t\ge0$ and $t=0$ corresponds to $12:00$ PM (noon): $$ In my experience, there are two basic forms of this sort of thing, and neither one is really being posed hypothetically. 80&=20t Somehow, we have to represent the time difference in their departure in one or both of the equations. 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. Hello highlight.js! Once you get to the point where you know the total travel times of both trains and their travel times, you could calculate how far each one went and find the exact location where they meet.
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". Train A leaves at time $t_{A0} = 0$ traveling at $40$ mph. d2=total distance - d1. 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. In other words, when are both trains the same distance away from Town A. A train leaves point A at 5 am and reaches point B at 9 am. It would be a nice slam dunk to pull on people at a party if there's a simple way to figure it out.
Two trains leave different cities heading toward each other at different speeds. Why do people say the Pakistani government has failed because the army is interfering with politics?
Substitute that back into the speed of the trains to get: 100 mph * 0.88 = 88 miles west of Atlanta, 75 mph * 0.88 = 66 miles east of Birmingham, 88 + 66 = 154 (I rounded the .88, and it was actually 0.88235294117) so that checks out. They both went for 3 hours. If we write our equation for Train #1 as d = 60x + 120, now both this equation and the equation that we have for Train #2 refer to the distance each train is away from Town A, starting at 7AM (the first time that BOTH trains are traveling). If you're being asked this in an informal context and want to solve this in your head as a party trick like the OP suggests, an easy way to do it is to take one train, and ask roughly what fraction of the total speed belongs to that train.
in another, the trains crash into one another. strangers build memorials to the wreckage; they leave crosses by the tracks, silk flowers that the wind drags away. Why does 60 Hz mean 60 refreshes and not 120? The sum of both distances is the total distance. That means it will have covered about two thirds of the total distance at the time the trains meet. Also, the time zone difference shouldn't matter. Don't Panic! If someone left at $t$ and you leave H hours later, why your time is $t - H$?
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. Can anyone dumb it down for me further? What is the EXACT time that the collision will occur? For that joke, you don't even need any actual numbers, so if the question doesn't have numbers involved you can tell right away it's a joke and not a problem. You want to make sure you get that before going on. If the distance between these two cities is Z miles, where do they meet?'. In other words, $S/60 = S/40 -2$, so $S=240$ (miles). The simple way of doing this is to use the distance equation, Distance/Time = Rate. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa.
So, the combined speed of both trains is 170 mph, which means that the can cover 150 miles in 150/170 = 0.88 hours. No packages or subscriptions, pay only for the time you need. The trick with word problems is to pick them apart to see what you know, then build equations that you can solve. I got 6 P.M. but the answer key says 4 P.M.? Why is the centre of mass of a semicircular wire outside the body? Here is where i get stuck.
Let's say train A and train B are 300 miles apart. Divide the distance between their starting points by the closing speed, to get how long it'll take them to meet. Mathematics Because I've seen the question posed hypothetically a hundred times, but never seen it … Train A goes 120mi from 5-7am, leaving a 335mi gap ... after 7am, the gap closes at 130mph ... "stair-step" ... 8am, 205mi left ... 9am, 75mi remains ... 9:30am, 10mi left -- need 1/13 more of an hour ... 60min/13 = 4.6 mins ==> crash at 9:34:35 :), Patricia S. These are the same location. Train B leaves at time $t_{B0} = t_{A0} + 2 = 2$ traveling at $60$ mph. Once you get it, it'll seem almost obvious. Gene G. Edit: you could be picky and ask what if they were only 50 miles away instead of 300? 40t=60(t-2)\implies\\ Train A went a grand total of 60×3=180 miles.
Where do the trains meet? Danielasdf B. Must one say "queen check" before capturing a queen? If you can name the actual geographic area that will turn out to be, even in general terms, you look like a genius. Now both trains are moving, one traveling at 60 mi/hr and the other at 70 mi/hr.Their closing speed is just 60 + 70 = 130 mi/hr, and the total distance to go is 335 mi. 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). Where are the trains?
The math still works because 50/100=1/2. It asks how much time until they meet. Choose an expert and meet online. Algebra Manipulation Contest Math Problem.
Lots of good answers here. When and where do they collide? 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. They will meet each other 2 hours after they both depart. head on, full speed, in broad daylight. For Free, = 5:00 + 4.5769 = 5:00 + 4:00 + 0:34 + 0:00:37 = 9:34:37, ALL MY GRADE 8 & 9 STUDENTS PASSED THE ALGEBRA CORE REGENTS EXAM. It's the same point because the total track is 180+120=300 miles long. Try it! Train B starts in Birmingham, and travels east at 70 miles per hour. In this problem, we know that one train starts two hours before the other one and travels at a known rate. A travels towards the train station B is at, while B travels towards the train station A is at. So they crash in 300/100=3 hours. Your calculation of 6pm as the time of passing is correct.