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

 

 

 

Subtract 60x from both sides.

 

 

Divide both sides by 120

 

 

 

So she was stuck in traffic for 1 hour.

 

Check. 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.

 

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