SOLUTION: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle. Not sure how to do these word probl

Question 170727This question is from textbook intermediate algebra
: Steve traveled 600 miles at a certain speed. Had he gone 20mph faster, the trip would have taken 1 hour less. Find the speed of his vehicle.
Not sure how to do these word problems and will appreciate any help, so far I have a B in class :) This question is from textbook intermediate algebra

Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
well we know that distance equals rate times time. d=rt
:
In our case distance is the same under both scenarios 600 miles.
:
what is different is the speeds and thus the times as speed and time are inversely related.
:
so in the first trip lets call the rate r and the time t.
in the second scenario the rate would be r+20 and the time is t-1.
:
600=rt....................eq 1
600=(r+20)(t-1)...........eq 2
:
lets rewrite eq 1 as t=600/r and place that value into eq 2
:

multiply by r
multiply factors on right side of eq
combine like terms on one side of equation

:
throw out the negative speed
:
so speed on first trip is mph and on second trip is mph
:

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=48400 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 100, -120. Here's your graph:

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