You can
put this solution on YOUR website!you have to set this up as 2 different parts of a lonnnnnnnnnggggggg trip.
:
lets call the 2nd part of the trips rate r and time t and
:
so then we will call the first part of the trips rate r+5 and the time 8-t(total time minus 2nd part of the trips time(t))
:
so
75=rt......................eq 1
60=(r+5)(8-t)..........eq 2
:
lets rewrite eq 1 to t=75/r and plug t's value into eq 2
:
60=(r+5)(8-(75/r))
:
60=(r+5)((8r-75)/r).........now multiply both sides by r
:
60r=(r+5)(8r-75)
:
:
throw out negative answer
:
therefore rate on 75 mile part of trip is 15mph
:
rate on 60 mile part of trip is
mph
:
| Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) |
Quadratic equation  (in our case  ) has the following solutons:
For these solutions to exist, the discriminant  should not be a negative number.
First, we need to compute the discriminant :  .
Discriminant d=21025 is greater than zero. That means that there are two solutions:  .
Quadratic expression  can be factored:
Again, the answer is: 15, -3.125.
Here's your graph:
 |
(