4. Linda drove to King City which is 210 miles away. For the first 30 miles she got stuck in traffic, but after that the traffic was fine. Fortunately, the time she spent on the open road was 2 hours more than the time she was stuck in traffic. If her average speed on the open road was twice as fast as her speed in traffic, how long was she stuck in traffic?

Let   x = how long Linda was stuck in traffic.

Then   x + 2 = how long she spent on the open road.

If Linda was stuck in traffic for 30 miles, the time she was stuck in traffic was 30/x. If it is 210 miles to King City, and she was stuck in traffic for 30 miles, then she was on the open road for 180 miles. Therefore the time she spent on the open road would be 180/(x + 2). We can now translate the sentence:

"Her average speed on the open road was twice as fast as her speed in traffic"

as

or

Cross multiply.

180x = 60(x + 2)

180x = 60x + 120

Subtract   60x   from both sides.

120x = 120

Divide both sides by 120

x = 1

So she was stuck in traffic for 1 hour.

Check: If she was stuck in traffic for 1 hour, then she must have spent 3 hours on the open road. If she spent 1 hour at 30mi/hr and 2 hours at 60mi/hr, she would have gotten 30 miles at 30mi/hr and 180 miles at 60mi/hr. That totals to 210 miles which is given as the distance to King City.