Time and Distance question

[bluebooger]

been awhile since I've done this so I may be doing it wrong, but this is what I think

the equation of a line is
y = mx + b
where m is the slope and b is the y intercept

on the graph x is the hours and y is the miles

why ?
because the speed is

miles
-----
hour

and slope is

change in y
-----------
change in x

so miles must be y and hour must be x

the equation for car A is
y = mx + b
y = 50x + 1

we use 1 for the y intercept because car A has a one mile headstart
so its starting point is not at the origin, but one mile ahead

the equation for car B is
y = 51x + 0
or
y = 51x
we use 0 for the y intercept because car B is starting at point zero

so if y = 51x in the 2nd equation, then substitute 51x for y in the first equation

51x = 50x + 1

subtract 50x from both sides
1x = 1

divide both sides by 1
x = 1

x is one so in one hour B catches up with A

now watch somebody smart come along and show how this is completely wrong