5. Linda drives from Ukiah to the East Bay. She averages 60mi/hr on the freeway, but when she gets to the East Bay, the freeway is clogged with rush hour traffic. Fortunately, she knows the East Bay, and knows how to get to her destination on surface streets. Unfortunately, she can only average 30mi/hr on the surface streets. The trip was 150 miles long and it took her 3 hours. How long was she on the freeway and how long was she on the surface streets. How far did she drive on the freeway and how far did she drive on the surface streets?

The first step in solving word problems is to define the unknown. If we let the unknown be what they're looking for, in this case there are two unknowns: the time she was on the freeway, and the time she drove on the surface streets. We could set this problem up with two unknowns.

Let   x = the time on the freeway

y = the time on the surface streets.

The fact that the entire trip took 3 hours gives us the equation

x + y = 3

We can solve this equation for   y

y = 3 - x

to express   y   as a function of   x.   As a result, we do not need to use   y. Wherever we need to use the time on the surface streets, we can use the expression   3 - x   instead.

Your authors suggest that we make use of a   d = rt   table

As soon as we get two columns filled in, we can fill in the third column by using the appropriate equation. In this case that is   d = rt.

Now we can express the fact that the total distance was 150 miles as

60x + 30(3 - x) = 150

Remove parentheses

60x + 90 - 30x = 150

Combine the   x   terms and transpose the 90 to the other side of the equation

30x = 150 - 90

Combine and divide by 30.

or

x = 2

She spent 2 hours on the freeway so she must have been on the surface streets for 1 hour.

Check:

If she spent 2 hours on the freeway at 60 mi/hr, she would have traveled 120 miles on the freeway. If she spent an hour on the surface streets averaging 30 mi/hr, that would have been an extra 30 miles for a total distance of 150 miles.