Time and Distance question

[CLEP101]

Car "A" is traveling at 50 miles an hour.
Car "B" is traveling at 51 miles an hour.
Car "B" is 1 mile behind care "A".

How much time will it take for car B to be even with Car A at the current speed.
How many miles will be traveled before car B will be even with Car A at the current speed.

What are the answers, but also what is the formula to get the answers?

Thanks in advance.

[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

[Flelm]

It's right, but could be done without the line stuff.

distance = time * velocity

Car A: x = t * 51
Car B: x - 1 = t * 50

(Car B travels 1 mile less in the same amount of time)

Two variables, two equations. You can do a number of solving methods, but I'll just substitute.

(t*51) - 1 = t*50
t-1 = 0
t = 1

Time is 1 hour.

To find the distance, use t in either of the above equations.

x = t * 51
x = 1 * 51
x = 51

51 Miles.

[CLEP101]

After reading both your posts I realized that I really really hate math. I don't know why that equation was bothering me, but it was and I couldn't get to the answer. Thanks to the both of you for helping me out.

[slefoll7]

It is way easier than that. Car B will take 60 minutes to catch up with car A, because it is going 1 mph faster. The absolute speed of each car does not matter, only the relative speed. Car B will also go 51 miles in that 60 minutes, because that is how fast he is going. Car A will go 50 miles, because he started 1 mile ahead of car B. No need for any equations or anything.

[bluebooger]

It is way easier than that. ...

yeah, but you had almost 2 years to think about it