SOLUTION: I can't figure the following quadratic question: Tim and Brad leave at the same time. They drive in different directions. Tim is slower than Brad by 8mph. After an hour, they ar

Question 78750: I can't figure the following quadratic question:
Tim and Brad leave at the same time. They drive in different directions. Tim is slower than Brad by 8mph. After an hour, they are 85 miles apart. What is Brad's speed?
How did the equation get to be 2x(square)-16x-7161? Someone please help.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
What the problem neglected to tell you was that Tim and Brad are traveling at 90 degrees
to each other. For example, Tim is driving north and Brad is driving east ... or some
similar arrangement ... one going south and the other one west, one going east and the other
one going south, one going west and the other one north..
.
That being the case, the Pythagorean theorem describes the distance between. Tim and Brad
are driving along separate legs of a right triangle (for example, one on the x-axis and
one on the y-axis). Suppose they both start at the origin (0,0) and Tim goes north up
the y-axis while Brad heads east (to the right) on the x-axis. The distance between them
is the hypotenuse of the right triangle ... which is the distance represented by a straight
line drawn from one of the cars to another. If you sketch this out, you will see
that Tim and Brad are on the legs of a right triangle and the line connecting the cars
is the hypotenuse of that triangle.
.
Hopefully that makes sense to you. Now to solve the problem.
.
Since the problem asks you to solve for Brad's speed, you can call his speed B. Then
Tim's speed (according to the problem) is 8 miles per hour less than Brad's so you can
call Tim's Speed (B - 8).
.
The distance each travels on his leg can be calculated by multiplying the speed times
the time. (Just suppose Tim were traveling at 40 miles per hour. The distance he travels
in two hours can be calculated by multiplying his speed of 40 mph times 2 hours to get
a total distance of 80 mph. This example is just so you can get the concept of distance
equaling the speed times the time.)
.
Brad's distance from the origin is B times t where B is his speed and t is the one hour
specified in the problem. So in this case B*t = B*1 = B. After 1 hour Brad is B miles
east of the starting point. Meanwhile, Tim is driving north at a speed of (B - 8) mph.
In 1 hour the distance he goes is (B - 8) times 1 or just (B - 8) miles.
.
So the two legs of the right triangle are B and (B - 8).
.
The Pythagorean theorem tells you that the sum of the squares of these legs is equal
to the square of the hypotenuse (the distance between the cars). In equation form
you can write this as:
.

.
If you square the (B - 8) and the 85 on the right side this equation becomes:
.

.
Combine the terms on the left side to get:
.

.
To get this quadratic equation into standard form, subtract 7225 from both sides of the
equation. When you do that you get:
.

.
That's the equation you need. You didn't ask for help in solving this, but as a clue,
this equation does not factor so you need to use the quadratic formula (which is a shortened
version of completing the square).
.
As a check, you should find that the two answers you get for Brad's speed are about 63.971
mph and -55.971 mph. The latter represents backing up ... so ignore it. The answer is
that Brad is going approximately 64 mph and Tim, therefore, is going 8 mph less which
is about 56 mph.
.
I haven't checked these answers, but they should put you in the ballpark. Check to see
is pretty close to .
.
Hope this is the insight you needed to get a handle on this problem.
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