2 trains, 1 track, and a race to catch up-how long will it take? Most people get it wrong!

[@richardgrant5844]

2 hours assuming the 90 mph train leaves exactly one hour after the 60mph train each train will travel have traveled 180 miles. It's an in your head question.

[@JohnDoe-ok5wo]

Im guessing 2 hrs. Since 2nd train gains on 1rst train at 30 mi per hr it will take 2 hrs to make up 60 mile head start. Now ill see how John does it with algebra.

[@vincentrobinette1507]

I used a more simple method. I took the difference in speeds, then multiplied it by the 60 minute head start. The closure speed is 30 MPH, so it takes 2 hours, to cover the 60 mile head start. (no calculator necessary) It's the relative speed and distance between them, that makes the difference.

[@stevendebettencourt7651]

Well, according to Zeno’s Paradox, since the 60 MPH train has a head start, the 90 MPH train will never catch it. By the time it has caught up to the 60 MPH train, that train has moved forward more, so it has to catch up. And no matter how many times the second train catches up, the first train keeps moving forward, so it never passes the first train. However, we know this is not true, so, how do we do this? Well, we can create equations for how far the two trains travel at time t (let’s have t be in minutes): L_1(t) = 60t L_2(t) = 0 if 0=0). Besides a trivial equality at t=0, we need to find where these two equations are equal: L_1(t) = L_2(t) And for our purposes, this means: 60t = 90(t-60) 90t - 5400 = 60t 30t = 5400 t = 540 / 3 t = 180 So, if my math is right, three hours after leaving the station, the first train will be overtaken by the second, or from the perspective of the second train, it passes the first train two hours after it leaves. 3 hrs * 60 mi/hr = 180 miles 2 hrs * 90 mi/hr = 180 miles. Yeah, checks out. Now, why does Zeno’s Paradox not hold?

[@eric4709]

Exactly the question i posed!!!

[@brianwade4179]

Zeno does not realize that in each iteration of his thought experiment, less time passes. Each time interval is shorter than the previous one.

[@EricWells-s2p]

When the second train leaves from the same location the first train left one hour earlier, the first train will have already traveled 60 miles. Two hours later, both trains will be exactly 180 miles from their starting point.

[@3Deez3]

2 hrs. Mental math. The 90mph will travel 90miles its first hr while the 60mph will be on its 2nd hr and traveled 120miles. After the 90mph train’s 2nd hr., it will travel twice as far, 180miles. The 60mph train will be on its 3rd hr and traveled 60x3 miles. 180mile. So 2 hrs to catch up.

[@don911donny9]

You didn’t make it very clear that the 90mph train departs 1hr after the 60mph train has begun its journey, it had me thinking so when does the 90mph train start it journey; otherwise it’s pretty straightforward.

[@johnlakin5895]

First thing l think in the morning…..”l wonder what the you tube math man’s got for me today. 😊

[@panlomito]

Distance1 = 60 mph . 1 hr + 60 mph . t miles and Distance2 = 90 mph . t miles Ketchup at D1 = D2 so 60 + 60t = 90t -> 60 = 30t -> t = 2 hour Check: 60 + 60 . 2 = 180 miles and 90 . 2 = 180 miles.

[@lizardfirefighter110]

How can I solve this problem before playing the version to see if I got the answer, if in the description I do not know how far apart the trains are at the start?

[@chrisdissanayake6979]

Answer: The two trains meet in 2 hours. ---------- Let the 1st train that travels at 60mph be train A. Let the 2nd train that travels at 90mph be train B. Train B leaves 1 hour after train A. Let the time taken by train B to catch up to train A be t hours. The distance travelled by train A in t hours = 60t miles. But, the train A had already travelled for 1 hour, at 60mph, before train B started to travel. Therefore, the total distance train A had travelled when it met train B = 60t + 60 miles The distance train B travelled in t hours = 90t miles. Since both train A and train B had travelled the same distance when they met each other, 90t = 60t + 60 30t = 60 t = 2 hours

[@eric4709]

After one hour.. the 60mph train has travelled 60 miles ( 60 miles/hour * 1 hour = 60 miles) At exactly this 1 hour has passed, the second train starts moving on a separate track moving towards the first train Assuming the second train instantly reaches 90mph - then both trains are moving with a closing speed between them of 90-60 mph = 30mph ( ignoring relativistic effects lol!) In order to close the gap of 60 miles, this will take, at a closing speed of 30mph = 60miles / 30 miles / hour = 2hours The fact that both trains are moving doesnt matter.. ...... Imagine you are in one of the trains and you can ONLY see the other train... you cannot therefore tell or measure what absolute speed you are travelling at... you can only measure the relative speed between you and the other train. Thus...If you are on the second train.. you can only conclude that you are moving at 30mph relative in a direction towards the first train..... And...... For all you know... the second train could be standing still!! All you know is you are moving at 30mph relative to the other train. So it is going to take you 2 hours to traverse a distance of 60 miles to meet the seond train An interesting 2nd question is: How far has each train travelled when they meet? ( for clarirty - this is the distance from the starting point to the point of meeting... not the sum of the distances both trains have travelled)

[@eric4709]

Actually.. do the trains ever meet? See zeno's paradox ( hare and the tortoise)

[@jdp0359]

Yes he did! He very clearly stated it.

[@eric4709]

​@@jdp0359 I know that... but as an interesting thought experiment.. look at zenos paradox... ( 1/2+1/4 +1/8 .... to infinity)

[@russelllomando8460]

2 hours to catch-up. at 180 miles train 1 = 60 + 120 train 2 = 180 thanks for the fun

[@mauriziograndi1750]

As usual something easy camouflaged as complicated. The second train will take 2 hours to cover the distance the first train covers in 3 hours. Easy. But he didn’t say the second train started 1 hr later.

[@Skullmiser]

I got 2 hours. 60+60x=90x 2+2x=3x 2=x

[@genelowry5666]

It will take two hours.

[@jald910]

Agree