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 author suggests that we make use of a d = rt table

 

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.

 

completed d=rt table

 

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.

(30x)/30=(60)/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.

 

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