Question

Math help needed.





A train leaves the station at noon. The train is 180 miles from its destination at 12:45pm and 90 miles from its destination at 2:15pm.

How far is the station from the destination?

At what time will the train reach the destination?

Answer 1

90 miles from its destination

Answer 2

Although not stated, there seems to be an assumption that the train is moving at a constant rate (speed). So it's distance from the destination and time t is a linear relationship.

Thus, you know 2 points on the line that describes the relationship. If d=distance (this is like your "y") and t=time in minutes since noon(this is like your "x") then you have the following points (t, d):

(45, 180)
(135 ,90)

So you can find a line. Then when t=0 you will have d when the train left the station - that is how far the station is from the destination.

When d=0 you will have the time (minutes) since noon that it takes to reach the destination.

Answer 3

You could also get the results in an "intuitive" way if you just look at the pattern of the distance vs. time. But the linear equation is a formal (and mathematically rigorous) way to approach it. :)