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.
The fact that the entire trip took 3 hours gives us the equation
We can solve this equation for y
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
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
Remove parentheses
Combine the x terms and transpose the 90 to the other side of
the equation
Combine and divide by 30.
or
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.