Two hours and twelve minutes. That's how long before you realize you're on the wrong train.
@devonwilson577611 ай бұрын
Greetings. The answer is 2.2 hours. We will determine the solution to this problem by using the formula D=VT in which D is the distance to be covered, V the velocity, rate of change of distance with respect to time, and T the time taken to cover the distance to be covered, travelled. Now, we must first realize that the rate of separation of the trains will be the individual speed of each train added together, (85+65) MPH. That is, the trains are separating from each other at a break neck speed of 150 MPH. Now, we are to determine how long this rate of separation will take for the trains to be 330 miles apart. The time will be determined by using our D=VT given above, and plugging in the known values gives 330=150T from which it is determined that T=330/150, and T=2.2 hours.
@dlkline2711 ай бұрын
Got 2.2 hours working in my head. Took about 15 seconds.
@deech1811 ай бұрын
Right? People here proud of doing things the long way
@williamniver606311 ай бұрын
I did, too. I would infer from both of our experiences that we are of a similar age. In the '60s and '70s I attended a very traditional boys' prep school. Hours of drills, loads of homework EVERY night, including weekends, and an embrace of rote memorization. Sounds barbaric, doesn't it? Requiring 12 and 13 year-olds to study Latin before taking on a modern language. Algebra in 7th grade, allowing for two years of calculus before going to college. No real "electives" either, no music , art, or drama classes EVER in eight years (5th - 12th), but you could choose a second year of biology or organic chemistry or physics on senior year, and English "electives" might be a choice between "17th Century French Dramatists' or "The Lost Generation: Fitzgerald, Hemingway, and Stein". But psychology, technology, anthropology, fuggetaboutit. Discipline was swift and effective: talk out of turn in class? 2" masking tape over my mouth at least for that class, but a second time = taped til lunch. Heard to curse or being sneaky breaking rules or wilfully disregarding standards? One of three paddles smacked across your ass, whether you were 10 or 19. Have a beef with another student? The combatants (and most the rest of their class) taken to the gym, strapped on (huge) boxing gloves, and the other kids forming a "ring" with one of the coaches as referee. Issues were resolved, then declared over, no further repercussions, combatants required to shake hands and publicly announce resolution of hostilities. On the other hand, there was the Junior-Senior smoking room, anyone could buy fresh jolt coffee for a dime before class, nearly every 10th - 12th grader free to leave campus at lunch, and minor things like underage drinking or seducing girls from the local public high school - and a few times the female faculty - went ignored, do long as you kept up your grades. The result: 100% of graduates accepted at four-year colleges or universities. Every year. For decades. Not one exception. And for the last 59+ years, I have never heard a single complaint from an alum. Not a peep. We DO decry the current day additions of art and music classes at the expense of woodshop, the explicit rejection of corporal punishment, and namby-pamby tobacco-free campuses. Tuition in 1970 was $1,650; in 2023, over $46,000. Did I mention doing most of these math review problems in my head?
@aebalc11 ай бұрын
I would give that answer a fail. No one tells time using a decimal system. As the problem is worded you would need to answer 2 hours 12 minutes.
@Tokinjester11 ай бұрын
@@aebalc there is a business discipline that uses the decimal system to calculate time tho' I used to be a Work Study officer and our stopwatches are marked with 100 _seconds_ per minute ...it makes calculations easier Also, 2.2 minutes is exactly how I calculated it 😉
@jacoblussier9998 ай бұрын
What do you want a fucking cookie
@danieldennis983111 ай бұрын
It will be 2.2 hours or 2 hours, 12 minutes as long as the trains are in the middle of the US because only there are the train routes that straight and flat for such long distances. (65+85)x=330 150x=330 x=330/150 x=2.2
@panlomito8 ай бұрын
That was my idea too: time = distance / speed (in units: hours = miles / miles per hour = miles . hours per miles = hours ) So time = 330 miles / (65+85 mph) = 330/150 = 33/15 = 11/5 = 2 1/5 = 2.2 hours = 2 hours plus 60 minutes . 2/10 = 2 hours and 12 minutes Units are important !
@kennethwright87011 ай бұрын
Rate*Time=Distance Combined Rate is 65mph+85mph=150mph, so 330mi/150mi/h = 2.2h
@terry_willis11 ай бұрын
It depends how long the trains are. Some freight trains are 1 or 1-1/2 miles long. When you ask "how far apart" which part of the trains are you referring to? The front of the engine or the rear of the caboose (or last car)? Or somewhere in between?
@richardowens90619 ай бұрын
They have not actually passed each other until the trains are no longer passing each other - which means, the rear of the last car of each train has to pass each other. How far apart the engines are is irrelevant for this particular word problem. The distance between the trains would necessarily be end to end. Of course, the word problem could have been made more complex by specifying the length of each car, the length of the engines, and how many cars in each train, the standard distance between each car, and which train was going what speed, and whether the distance should be between the engines or between the end of the last car of each train. It could further be complicated if the two trains began at rest beside each other and accelerated at different rates in each direction up to their stated speed. You could even introduce varying slopes for each train that reduced or increased their speed. The potential variables are, essentially, endless.
@GailUnderhill11 ай бұрын
Since you’re a math teacher, who uses the word “problem” so often; perhaps you could pronounce it correctly. It would be easier to listen to you speak. In your defense, you are probably tired of saying the word “problem”. However, we must listen to it repeatedly. Occasionally, you do pronounce it correctly. I admire your math skills. I struggle with algebra. However, I do enjoy grammar, literature, reading, foreign languages, history, geography, and spelling. God gave each of us talents, interests, and aptitudes for learning. Math is not an easy subject for me. I enjoy how you explain, in detail, the procedures to solve the problems. Thank you for your help! I really like your channel. With so many subscribers, it is clear that many people need help with math.
@m.h.647011 ай бұрын
Solution: Everything is relative... so it doesn't matter, if you have two moving trains with 65 and 85 mph or one moving train with 150mph (=65 + 85) and one stationary train. So we simply need to calculate, how long it would take a 150mph train to reach 330 mile: 330 mi/150 mi/h = 330/150 h = 2.2 h = 2 hours and 12 minutes
@nicholasb890011 ай бұрын
Your formula is slightly off. It should read 330 miles / (150 miles / hour) which equals (330 miles hour) / (150 miles) to get the proper units
@m.h.647011 ай бұрын
@@nicholasb8900 mi/h is the same as mph. it is one term. I only wrote it that way, so that it becomes clear, that mi cancel out and hours remain.
@nicholasb890011 ай бұрын
@@m.h.6470 yea I was being too nit picky. I blame it on the math KZbin channel I been binging on who harps on units.
@thomasharding183829 күн бұрын
Trains usually go north-east (or north-west) (n/e or n/w) or south-east (or south-west) (s/e or s/w) but usually east/west would be called North (or South). So, because the trains are traveling at a differential speed of 20 mph, it would take them 16.5 hours to open a distance of 330 miles between them. UNLESS, they are going in opposite directions! Then it would take 2.2 hours, because their differential speeds would be 150 mph. But their relative direction (same or opposite) is not stated, is it‽ (The preceding assumes common fixed points of measurement on each train, Engine to Engine, or Caboose to Caboose, and not the air gap between the leading Caboose and trailing Engine.)
@joekauffman288411 ай бұрын
2 hours and 12 minutes between Texarkana and Little Rock.
@Michael4371311 ай бұрын
Got in 3 mins. Freeze one train then relative speed = 150mph. Then time = distance/speed.
@kennethstevenson97611 ай бұрын
A more useable answer could be found by converting 330/150 = 33/15 = 2 12/60 = Two Hours and 12 minutes.
@HeatherDiMarco11 ай бұрын
2hr and 12 min assuming they are both really short trains and pass each other very quickly
@johnallen355511 ай бұрын
how long are the trains? - how is the apart mesuresd? (along the rail line or in a straight line) - if in a straight line, the curvature of the earth should be taken into consideration - We would need a map of the rail line as the rail line is most likely got curves etc in it. - Now, only the passing speed of the trains is provided, I am not aware of any piece of straight track with no stations that will allow for full unadjusted speed for the required distance. So, we likely do not know the average train speeds over the 3 hours By ripping in without thinking, numnuts comes up with an answer that, were the same process be applied in engineering would likely result in some one being killed or some other major stuff up.
@JonBernhards6611 ай бұрын
Dude, wake up! The earth has no curvature to measure! Earth is a topographical plane.
@richardowens90619 ай бұрын
Both trains are on tracks. So, regardless of whatever curves might be involved, the distance is necessarily going to be measured on the tracks. And, since the speeds are specified and remain constant, acceleration can be dismissed. And, the distance between the two trains is specified as 330 miles. Remember, we have only the information specified in the word problem - so, that is all we have to consider to come up with a correct answer.
@luillierstephane146311 ай бұрын
2.2 h ??!! I certainly wouldn't write it this way. I found 02:12 , 2 hrs and 12 min.
@GoofballFlyer11 ай бұрын
I use tenths of hours when recording my flying hours. The clock (aka Hobbs meter) in the airplane records time that way to make adding time easier than hh:mm. 0.2 hours = 0.2 x 60 = 12 minutes.
@Snap-Anzahl11 ай бұрын
Wouldnt it be faster to add the speeds together and divide them by 60. This would have them traveling at 2.5 miles per minute then divide the distance (330) by 2.5 = 132 min.
@ernestannang943510 ай бұрын
What if they are moving towards each other? What Will be speed(rate)?
@DominicMazoch11 ай бұрын
Suppose onr or both trains reach their endpoints before 385 miles?
@renenadeau32311 ай бұрын
One train going 150mph. 330/150= 2.2hrs.or 2hrs 12 min.
@adamglltt8911 ай бұрын
Add the speeds together. Divide the miles by the speed. 2hrs and 2 10ths of an hour. 2h12 minutes. Speed Distance Time triangle helps with these things.
@GoofballFlyer11 ай бұрын
This assumes the trains maintain their speed at the time of passing. That's highly unlikely, so state the assumption.
@raynewport93957 ай бұрын
We are only given the passing speed, so we have not enough information.
@keithschipiour468411 ай бұрын
Somebody forgot throw the switch trains were on same track had head on collision and did not pass each other .
@loneranger636111 ай бұрын
330/(85+65)=2.2 hours
@MathsMadeSimple10111 ай бұрын
They probably had to stop at multiple stations each. So impossible to answer
@russelllomando846011 ай бұрын
got it. in minutes 2 hr 12 min 12 min is .2 hours - 1/5th.
@MFisher734611 ай бұрын
Hours are not metric. 0.2 hours = 12 minutes.
@agentD9911 ай бұрын
2 hours 15 minutes give or take.
@williamkirkconnell730611 ай бұрын
16
@Real_LiamOBryan11 ай бұрын
I don't know why, but my brain thought .2 of an hour, obviously 1/5th of an hour, was 6 minutes, obviously 1/10th of an hour. This led me to think the answer was 2 hours and 6 minutes. Fail, brain.
@mylittlepitbull314311 ай бұрын
Real quick in my head I got 330/150 hours Which really is not too bad if you think about it. I might take the train next time.
@freeguy7711 ай бұрын
In Oct-Nov. 1966, I took the Last Train to Clarksville!
@mylittlepitbull314311 ай бұрын
@@freeguy77 did it take 2.2 hours
@tommykyle157011 ай бұрын
Easy problem
@richardkanavel435811 ай бұрын
2,2 hrs
@gennyshovel708311 ай бұрын
2hr 12 min
@andrewwhite103811 ай бұрын
2hrs 12mins
@chuckmoore821911 ай бұрын
2 hours and 12 minutes
@DelmarBrewer11 ай бұрын
2hours and 12 minutes
@kennethhubbard202711 ай бұрын
2 hours 12 min
@ec63311 ай бұрын
Fourteen minutes
@Real_LiamOBryan11 ай бұрын
Yep.
@andypandy993111 ай бұрын
2 hours 12 minutes
@jajapani11 ай бұрын
Love your videos, but for god sake, can you do it quick.
@Tokinjester11 ай бұрын
The whole point of the video is to teach people who don't know math, they need the explanation...just click on the end of the video to see if you're answer's correct, that's what most people do 🤷🏻♂️
Another case of this guy being unclear. If you got this on an exam as it is written, you wouldn't know if they were both going east to west or in opposite directions.
@JoeGator2311 ай бұрын
You asked the question wrong... I thought they were both traveling in the same direction, not diverging.
@keithschipiour468411 ай бұрын
This why I was never good at math . Because I dont care about any stupid trains or how far there apart . Same reason I am not a expert on monkey sex life .
@Tokinjester11 ай бұрын
Same reason you're not an expert in English too? [ *_they're_* apart ] 😂