SOLUTION: I have an assignment and it's about a fair race between two animal and I need to make their out come into a linear equation. First speed 45 mph second is 43mph. Can you please help

Algebra ->  Linear-equations -> SOLUTION: I have an assignment and it's about a fair race between two animal and I need to make their out come into a linear equation. First speed 45 mph second is 43mph. Can you please help      Log On


   

Question 1085554: I have an assignment and it's about a fair race between two animal and I need to make their out come into a linear equation. First speed 45 mph second is 43mph. Can you please help me
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You will have 2 equations that have the form:
[ distance ] = [ rate ] x [ time ]
+d+=+r%2At+
You are given the rates, which will be the slopes
of the straight lines. So you have:
+d+=+45t+ and
+d+=+43t+
---------------------------------------
The rates have units of miles/hr, so the
units of the 3 parts of the equations are:
[ distance in miles ] = [ rate in mi/hr ] x [ time in hrs ]
--------------------------------------------------
You can choose various values for +d+, and determine +t+
for example:
+d+=+45+ mi
+d+=+45t+
+45+=+45%2A1+
+t+=+1+ hr
-----------------
+d+=+90+ mi
+d+=+45t+
+90+=+45%2A2+
+t+=+2+ hrs
-----------------
So you have 2 points on the 1st line:
( 1, 45 ) and
( 2, 90 )
-----------------
Keep going like this for both lines, and
you can plot them.
-----------------
If the animals start a race together at the
same time, the slow one is always behind.
--------------------------------------
If you give the slow one a headstart, then
the fast one will catch up after a certain
time +t+
---------------------------------------
Here's a plot with the slow one having a headstart of
+10+ mi
+graph%28+500%2C+500%2C+-1%2C+5%2C+-10%2C+200%2C+43x+%2B+10%2C+45x+%29+
You can see they have to run many miles for the fast one to catch up.
Hope this helps