SOLUTION: A dreaded word problem. This is out of the Algebra textbook 5th edition by Dugopolski. Chapter 8.3 page 550 #85. Here's the problem: Erin was traveling across the desert on her bi

Question 235021: A dreaded word problem. This is out of the Algebra textbook 5th edition by Dugopolski. Chapter 8.3 page 550 #85. Here's the problem:
Erin was traveling across the desert on her bicycle. Before lunch she traveled 60 miles (mi); after lunch she traveled 46 miles. She put in 1 hour more after lunch than before lunch, but her speed was 4 mph slower than before. What was her speed before lunch and after lunch?
The answer is in the back of the book, and it is:
Before -5 + the square root of (265) or 11.3 mph;
After -9 + the square root of (265) or 7.3 mph
We are just completely confused about how to get the solution. We attempted to set it up in a distance=rate*time chart, but are not having any luck with that. Could you please show how to get a solution to this problem? Thank you very much in advance!!
Sandy :-)
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You need 2 equations, 1 for each part of the trip

given:
mi
mi
hrs
mi/hr
----------------------
Now I can rewrite the equations
(1)
(2)
This is 2 equations and 2 unknowns, so it's solvable
(2)
And, since ,
(2)
(2)
Now go back to (1)
(1)

plug this back into (2)
(2)
Multiply both sides by

This can be solved by completing the square

The left side is a perfect square

Take the square root of both sides

mi/hr
And, since

mi/hr

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