Homework question: Confused what the question is asking for.

Question

The question: Trains run along the Bettingland Line between Betson and Winsome (via Hope) roughly once per hour in each direction. It is proposed to increase the frequency to be one train every 15 minutes in each direction. A train from Betson to Winsome takes 50 minutes, whilst travelling from Winsome to Betson takes just 40, as it doesn’t have to wait at Hope for a connection. If the first train is to leave Betson at 0700 and the first train is to leave Winsome at 0715, how many trains are needed to run the service? How long will each train have to wait at each terminus?

What are the questions at the end asking me to find? Could I get an answer for this question just to see what it meant? Thanks :D

Answer 1

To run from Betson to Winsome takes 50 minutes, but the trains must leave every 15 minutes, so in an hour four Trains will leave from Betson to Winsome and there will be a slight delay (boarding and unboarding) at Winsome.  

 

From Winsome to Betson takes 40 minutes.  Again, the discrepancy between 40 minutes travel time and a 15 minute departure schedule means that there is a slight delay at Betson.

 

Notice that the first train out of Betson arrives at Winsome in time to be the fifth train out of Winsome.  The first train out of Winsome arrives at Betson in time to be the fourth train out of Betson.

 

            Betson     Winsome

:00          B1            W1

:15          B2            W2

:30          B3            W3

:45        (W1)           W4

:00        (W2)          (B1)

 

So, it takes a minimum of 7 trains to keep the schedule.

 

 

 

 

 

 

 

Answer 2

Draw a straight line (like a number line) with Betsome at one end, Winsome at the other, and Hope in the middle.

 

Draw a dot to represent a train at Betsome and another at Winsome.

 

Now, what they're asking is, if a train is supposed to leave each end every 15 minutes, but it takes 50 minutes in one direction and 40 in the other, you're going to need more than just 2 trains to keep up that schedule.

 

They're asking how many trains are needed on this line to keep up that schedule, and how long does each train wait at each end before its turn comes up. (It will be longer than the 15 minutes, since there will be more than 1 train at each end.)

 

One hint is, remember that when you go from Betsome to Winsome, you need to wait an extra 10 minutes.

 

Have fun! And remember, DRAW PICTURES.