Remember problems such as "if a train leaves London at 12:00 and goes north at 100mph....."?

Question

... and another leaves Glasgow at the same time but at 80mph southwards and the cities are ___ far apart, where and when do they meet?" How to solve? Were you meant to use algebra?

I used to use trial and error to see where they were at various times but my answer was always a bit off and my native wit never rewarded.

Answer 1

Yes you use algebra

Train A distance from london = 100 * t
Train B distance from London = 500 - 80 * t

When do these equal each other?

100t = 500 - 80t
180t = 500
t = 2.77 hours

Answer 2

the trick is that when both train meet, no matter what their speed was, they would have spent the same time t from the moment of departure till they meet and the distances they have travelled would sum up to the distance between L and G

London train will have traveled 100t miles and Glasgow train will have traveled 80t miles when they meet.
So, 100t + 80t = S ( distance between L and G)
given S, you will get t and 12:00 + t will get you the time.

Answer 3

Deduct 180 miles(London,100mph+Glasgow, 80 mph) from the actual distance for every hour traveled until it is zero. The hour at which distance is zero, is the hour the two trains meet.

Answer 4

Another way of looking at is that they have to cover 500 miles of track between them and their combined speed is 180mph, so the time for them to collide (ie when they have covered all the track!) is 500/180 = 2 and 7/9 hours.

No algebra needed.

Answer 5

let Sg=distance tavelled
by train from glasgow
=80*t
let Sl=distance travelled
by train from london
=100*t
let x= Sg+Sl
=distance between glasgow
and london
therefore,
x=80t+100t
=180t
hence,t= (x/180) hours

Sg=(4/9)*t (distance from G)
Sl = (5/9)*t (distance from L)
you now have the positions!
distance in miles

i hope that this helps

Answer 6

However, if one was a Pendolino and the other a Thames Train you may not wish them to meet.

Answer 7

I always thought the question was "Which train is closer to London when they pass?"
Did I miss something?

Answer 8

Distance = (velocity)*(time travelled)

Distance between towns = TD

TD = D1 + D2 = (V1)(time1) + (V2)(time2)

Use these basic sets of equations, plug in known times and velocities to find distances, or plug in velocities and distances to find times.

Answer 9

Yes use algebra it works wonders!