Question

Question 3) Suppose that a person drives 20 miles to work each day along a highway. In the morning the person drives the highway at the speed limit. In the evening there is lots of traffic and the person drives at 30 miles per hour slower than the speed limit. Their total commute time is 1 hour. What is the speed limit on the freeway? (HINT: Compose an Rational Equation to solve this).

Answer 1

The speed limit on the freeway is 60 miles/hour.

Explanation:

Suppose, the speed limit on the freeway is
`x` miles/hour.

We know that,
`Time= (Distance)/(Speed)`

So, the time required in the morning to drive 20 miles
`= (20)/(x)` hour.

Now, in the evening, the person drives at 30 miles per hour slower than the speed limit. That means, speed in the evening
`=(x-30)miles/hour`

So, the time required to drive 20 miles in the evening
`=(20)/(x-30)` hour.

Given that, the total commute time is 1 hour. So, the equation will be......

`(20)/(x)+ (20)/(x-30)=1 \\ \\ (20x-600+20x)/(x(x-30))=1 \\ \\ (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`

Using zero-product property, we will get.......

`x-60=0\\ x=60\\ \\ and\\ \\ x-10=0\\ x=10`

Here we can't take
`x=10`, as the speed in the evening will become negative for
`x=10`

So, the speed limit on the freeway is 60 miles/hour.