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Time and Distance question
#1
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.
[SIZE="1"][SIZE="3"][SIZE="2"]Excelsior College - DONE[/SIZE][/SIZE]
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[COLOR="DarkRed"][B][SIZE="2"]Thomas Edison State College - DONE[/SIZE]
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[SIZE="2"]Texas A&M University Central Texas[/SIZE]
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Quote: There are no stupid questions, only stupid people. "Mr. Garrison"[/SIZE]
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#2
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 Smile
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#3
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.
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#4
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.
[SIZE="1"][SIZE="3"][SIZE="2"]Excelsior College - DONE[/SIZE][/SIZE]
[SIZE="2"]AAS-[SIZE="1"]2009[/SIZE], BSLS-[SIZE="1"]2010[/SIZE] [/SIZE]

[COLOR="DarkRed"][B][SIZE="2"]Thomas Edison State College - DONE[/SIZE]
[SIZE="2"]BA in History[/SIZE]-[SIZE="1"]2011[/SIZE][/COLOR][/B]

[SIZE="2"]Texas A&M University Central Texas[/SIZE]
Master of Arts in History - 18/36 SH

CLEPs Passed
[SIZE="1"][SIZE="1"]Spanish, Freshman Comp, English Comp w/ Essay, Social Science & Hist, Info Sys & Comp App, Intro Sociology, Prin of Mngmt, American Gov , US History I, US History II, Western Civ I, Western Civ II[/SIZE][/SIZE]
DSSTs Passed
[SIZE="1"][SIZE="1"]Civil War & Reconstruction, Rise & Fall of Soviet Union, History of Vietnam War, Intro Modern Middle East, Western Europe Since 1945, Drug and Alcohol, Here's to Your Hlth, Intro To Comp, Prin of Sup, Technical Writing, Prin of Physical Science I[/SIZE][/SIZE]

Quote: There are no stupid questions, only stupid people. "Mr. Garrison"[/SIZE]
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#5
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.
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#6
(03-22-2018, 09:54 AM)slefoll7 Wrote: It is way easier than that. ...

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