SOLUTION: On a 135 mile bicycle excursion, Maria averaged 5 miles per hour slower during the last 75 miles than for the first 60 miles. The entire trip took 8 hours. Find her rate for the fi

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Question 237997: On a 135 mile bicycle excursion, Maria averaged 5 miles per hour slower during the last 75 miles than for the first 60 miles. The entire trip took 8 hours. Find her rate for the first 60 miles.
Answer by solver91311(24713) About Me  (Show Source):
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Let represent the rate during the 60 mile leg. Then is the rate for the 75 mile leg.

Let represent the time to complete the 60 mile leg. Then the time to complete the 75 mile leg must be

So



and



Solve the second equation for (left as an exercise for the student). Now you will have two expressions equal to . Set them equal and simplify. The result will be the following quadratic equation:



Factor and solve for . You will obtain two positive roots, but one of them will be < 5, and can be excluded because that would make meaning she went backwards during the 75 mile leg.

John