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algebra intermediate
Problem
One day, I decide to run to the park. On the way there, I run at a rate of miles per hour for hours. On the way back, I take the same path and jog at a slower rate of miles per hour so that it takes me hours to get home. Given that , what is ? Express your answer as a common fraction.
Solution
Since we know that the distance that I traveled to the park and the distance that I traveled to get back home are the same, and that distance rate time, we have that Solving this equation, we get the solutions and . Since must be positive, we have .
Final answer
\frac{8}{3}