5. Linda goes to visit a friend who lives in Lompoc. It is 390 miles
from Linda's house to her friend's house. When she came back, she
didn't stop, so it took her a half an hour less time and her average
speed was 5 miles per hour faster. How fast was she going when she
went down to Lompoc, and how fast was she going when she drove
First we define our unknowns. In this case they are looking for
how fast she was driving when she went down to Lompoc and how
fast she was driving when she drove back. We could set this up with
two unknowns, but since we know that she averaged 5 mi/hr faster
coming back we could
and then we would have that
Your author suggests we make up a d = rt table to organize our
Once we have two columns filled in we can fill in the third
column by using the appropriate form of the d = rt equation. In this
case we need to fill in the column for the time so we use the equation
Now the sentence "It took her a half hour less time to get back."
can be translated as
This gives us a rational equation. Clear denominators. The
smallest common denominator is 2x(x+5)
Multiply the 2x(x+5) by both terms on the right side.
Cancel and assemble the surviving factors.
Remove parentheses and multiply.
After subtracting 780x from both sides, transpose all the terms
to the left.
and set the factors = 0.
We get two answers. One is 60 mi/hr and the other one is -65
mi/hr. Of the two, 60mi/hr makes more sense. If she was driving to
Lompoc at 60 mi/hr then it would take her 6.5 hours .If she came
back averaging 5 mi/hr faster then it would take her 6 hours which
would be 1/2 hour less time, and the answer checks.
The answer of -65 mi/hr would take a little more imagination
to check. It would mean that she was driving to Lompoc at 65 mi/hr
backwards. If she were driving backwards then she would have been
in Lompoc 6 hours ago. To get her speed coming back, adding 5
mi/hr to -65 mi/hr would give us a speed of -60 mi/hr, and it would
then take her -6,5 hrs which is 1/2 less than -6 hours. However,
most authors would have us reject such an answer as being
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