Converting a table into a system of three equations

Question

The route of a train travelling from station A to station D passes through Station B then station C. The table below gives the time (in hours) the trip will take if the given speeds (km/h) are maintain between each station. Determine the distance between each station by:

Station A to B Station B to C Station C to D Total time (hr)

90km/h 60km/h 60km/h 3

60km/h 80km/h 40km/h 4

40km/h 80km/h 50km/h 4

a) Define three variable and then express the problem as a system of three equations in terms of A, B and C using the information given.

What figures would be used in the system of three equations to allow for calculation of the distance between each station?

Answer 1

Let A, B and C be the variables representing the starting point of each segment.

The numbers in the table will be the DENOMINATOR in the coefficient of the respective variables.

The numbers 180, 240 and 400 will be the numbers needed to make the coefficients into integers in the respective equations.

Once that is done the system can be solved by several different methods, but in today's world the easiest and most direct thing to do would be to put the numbers into a spreadsheet which can invert the matrix almost instantaneously! In my opinion there is no excuse for solving messy systems of equations manually once you have seen how it can be done.