## Word problem: A train is travelling from A to B.

Simplificatation, evaluation, linear equations, linear graphs, linear inequalities, basic word problems, etc.
Luke53
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### Word problem: A train is travelling from A to B.

A train is travelling from A to B. After it travelled for one hour, it stops for one hour and then continues it's voyage with a speed that is equal of 3/5 of the initial speed. It arrives at B with a delay of 3 hours . If the train would have stopped 50 km further than the point where it first stopped, it would have arrived 1h 40 min earlier. Find the initial speed and the distance between A and B.
Sorry, made a correction, (I forgot something, the train stops for one hour).

I think I finally found the solution, the initial speed would be 50 km/h and the distance between A and B 275 km, (and the travelling time without delay would be 5.5 hours).
Anyway, thanks for the help, (and sorry for ignoring the one hour stopping time of the train in this word problem).
Greetszzz.
Luke.
Last edited by Luke53 on Sat Apr 09, 2011 4:21 pm, edited 2 times in total.

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: Word problem: A train is travelling from A to B.

You can see how to do this kind of problem by looking here.
A train is travelling from A to B. After it travelled one hour, it stops and then continues it's voyage with a speed that is equal of 3/5 of the initial speed. It arrives at B with a delay of 3 hours . If the train would have stopped 50 km further than the point where it first stopped, it would have arrived 1h 40 min early. Find the initial speed and the distance between A and B.
So pick a variable for the original (fast) speed, like 's'. The distance is some value 'd'.

Make an expression with the variable so the expression means 'three-fifths of fast speed'.

If there had been no stop, then the time (from 'd=rt') would have been t=d/s.

Now take the two parts of the actual trip. The first part is 1*s = s. The rest of the distance is d-s. The rate will be (3/5)s. Then the time will be the first hour, plus the time (from 'd=rt') for the rest, which is (d-s)/((3/5)s). Since this is three hours more than usual, the time is d/s + 3. Use this to make an equation.

Do the same sort of thing for the 'if the train had stopped sooner' part. This will give you two equations with two variables, so you can solve.

If you get stuck, please reply with what you've done so far. Thanks!

Luke53
Posts: 54
Joined: Sun Mar 13, 2011 9:46 am
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### Re: Word problem: A train is travelling from A to B.

distance(ab) = d(ab); v = initial speed; t = normal time of arrival.
d(ab) = v * t
first case:
d(ab) = v *1 + 3/5 *v *(t+3 -1)
d(ab) = v + 3/5 v * (t+2)
d(ab) = v + 3/5 * v *t + 6/5 * v
second case:
d(ab) = v + 50 + 3/5 *v * (t +3 -1 - 1.66)
d(ab)= v + 50 +3/5 v *t + 1/5 * v
since the distance is the same:
v + 3/5 v *t + 6/5 *v = v + 50 + 3/5 v*t + 1/5 *v
5/5 * v = 50 ; so v = 50 km/h (initial speed).
Is this correct so far?
Luke

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
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### Re: Word problem: A train is travelling from A to B.

If your answer is correct, then it will work in the original problem. Does it?