SOLUTION: A car travels 180mi, a second car, traveling 15mi/h faster than the first car , makes the trip in 1 hr less time. Find the speed of each car.

Question 169541: A car travels 180mi, a second car, traveling 15mi/h faster than the first car , makes the trip in 1 hr less time. Find the speed of each car.
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
distance = rate multiplied by time. let r and t be rate and time of 1st car
and r+15 and t-1 be rate and time of 2nd car.
:
180=rt----------->t=180/r....eq 1
180=(r+15)(t-1)...eq 2
:
take t's value from eq 1 and substitute it into eq 2
:

:
....multiply by r
....distribute right side
:

:
use quadratic formula

throw out negative value
:
rate of 1st car
rate of 2nd car:

Solved by pluggable solver: SOLVE quadratic equation with variable

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=11025 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 45, -60. Here's your graph:

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