Welcome! You are encouraged to register with the site and login (for free). When you register, you support the site and your question history is saved.
Review: Frederique's Trip
Explanation
We can use a combination of analysis by cases and algebra.
If 
,
she traveled half the distance at 40 miles per hour and half the distance at 60
miles per hour. The average distance will be total distance divided by total
time. Let's call the total distance D.
Then the partial distances are 
and ,
and the corresponding times are
and 
so:
The D's cancel
out; the total distance has no bearing on the answer.
We can see that x affects
the share of eighths that go over the 40 in this denominator versus over the
60. We can cancel all fractions except one by multiplying top and bottom by 8
and 120:
The 4's correspond to x
and 
.
We can plug them back in:
The correct answer is (E).
If you believe you have found an error in this question or explanation, please contact us and include the question title or URL in your message.