Answer:
 54.2 mph
Step-by-step explanation:
Since the drivers leave at the same time and travel in directions 90° from each other, their separation speed can be found using the Pythagorean theorem. Let c represent Cynthia's average speed. Then (c-10) will represent Tim's average speed. Their combined separation speed is 70 miles per hour, so we can write ...
 70² = c² +(c -10)²
 4900 = 2c² -20c +100 . . . . eliminate parentheses
 c² -10c -2400 = 0 . . . . . . . . divide by 2; put in standard form
 (c -5)² -2425 = 0 . . . . . . . . . rearrange to vertex form
 c = 5 ±5√97 . . . . . . . . . . . . solve for c, simplify radical
 c ≈ 54.244 ≈ 54.2 . . . . . . . use the positive solution
Cynthia's average speed was 54.2 miles per hour.
