When is the denominator of the rational expression equal to 0 ?
A
a
3000+500x/3240+540x
B
b
Simplified Rational Expression: 2527 Explanation: The distance traveled by the first airplane is less than the distance traveled by the second airplane.
C
c
Condition: x=- 6 What does it tell us about the two airplanes? The first airplane would travel for 0 hours and the second airplane would travel at a rate of 0 miles per hour.
Practice makes perfect
a
First, let's calculate the distance traveled by the first airplane and the distance traveled by the second airplane. To do so, we will use the given formula.
d=rt
Here, r is the rate and t is the time. We know that the first airplane traveled at a rate of 500 miles per hour for a time of (6+x) hours. Let's substitute these values into the formula.
The first airplane traveled a distance of 3000+500x miles. The second airplane traveled at a rate of (540+90x) miles per hour for a time of 6 hours. Let's calculate the distance traveled by the second airplane.
The second airplane traveled a distance of 3240+540x miles. Knowing the distances traveled by each plane, we can calculate the ratio of the distance traveled by the first airplane to the distance traveled by the second airplane.
Distance traveled by the first airplane/Distance traveled by the second airplane
Let's substitute the distance traveled by the first airplane, 3000+500x miles, and the distance traveled by the second airplane, 3240+540x miles.
Ratio=3000+500x/3240+540x
We can see that both the numerator and the denominator contain the same factor, (6+x), so we can cancel it out. Let's also simplify the remaining expression as much as possible.
We have that the ratio of the distance traveled by the first airplane to the distance traveled by the second airplane is 2527. Therefore, the distance traveled by the first airplane is less than the distance traveled by the second airplane.
c
We want to determine when the rational expression found in Part A is undefined.
3000+500x/3240+540x
Recall that a rational expression is undefined when its denominator is equal to 0.
3240+540x=0
Let's solve the above equation for x.
