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.
