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algebra intermediate

Problem

At the beginning of my bike ride I feel good, so I can travel 20 miles per hour. Later, I get tired and travel only 12 miles per hour. If I travel a total of 122 miles in a total time of 8 hours, for how many hours did I feel good? Express your answer as a common fraction.
Solution
Let equal the number of hours that you felt good riding. Then, hours were spent traveling at 20 mph, and hours were spent traveling at 12 mph. During this time, a total of 122 miles was traveled. Remembering that , we can add the two distances, set this equal to 122 miles, and solve for as shown:
Final answer
\frac{13}{4}