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Beatrice traveled the last 220 miles of the trip at 55 miles per hour. The entire trip covered 430 miles and took 7 hours. What was her rate for the first 210 mile?

Guest May 4, 2017
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Beatrice traveled the last 220 miles of the trip at 55 miles per hour. The entire trip covered 430 miles and took 7 hours. What was her rate for the first 210 mile?

 

Let Beatrice's average speed for the first 210 miles = S

 

220/55 + 210/S

Solve for S:
4 + 210/S = 7

Bring 4 + 210/S together using the common denominator S:
(2 (2 S + 105))/S = 7

Multiply both sides by S:
2 (2 S + 105) = 7 S

Expand out terms of the left hand side:
4 S + 210 = 7 S

Subtract 7 S + 210 from both sides:
-3 S = -210

Divide both sides by -3:
Answer: |S = 70 - miles per hour, her speed for the first 210 miles.

Guest May 4, 2017
edited by Guest  May 4, 2017
edited by Guest  May 4, 2017

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