Respuesta :
Answer:
The speed limit on the freeway is 60 miles/hour.
Step-by-step explanation:
Suppose, the speed limit on the freeway is [tex]x[/tex] miles/hour.
We know that, [tex]Time= \frac{Distance}{Speed}[/tex]
So, the time required in the morning to drive 20 miles [tex]= \frac{20}{x}[/tex] hour.
Now, in the evening, the person drives at 30 miles per hour slower than the speed limit. That means, speed in the evening [tex]=(x-30)miles/hour[/tex]
So, the time required to drive 20 miles in the evening [tex]=\frac{20}{x-30}[/tex] hour.
Given that, the total commute time is 1 hour. So, the equation will be......
[tex]\frac{20}{x}+ \frac{20}{x-30}=1 \\ \\ \frac{20x-600+20x}{x(x-30)}=1 \\ \\ \frac{40x-600}{x(x-30)}=1\\ \\ x(x-30)=40x-600\\ \\ x^2-30x=40x-600\\ \\ x^2-70x+600=0\\ \\ (x-60)(x-10)=0[/tex]
Using zero-product property, we will get.......
[tex]x-60=0\\ x=60\\ \\ and\\ \\ x-10=0\\ x=10[/tex]
Here we can't take [tex]x=10[/tex], as the speed in the evening will become negative for [tex]x=10[/tex]
So, the speed limit on the freeway is 60 miles/hour.
