Tim and Cynthia leave Cynthia's house at the same time. Tim drives north and Cynthia drives west. Tim's average speed is 10 mph slower than Cynthia's. At the end of one hour, they are 70 miles apart. Find Cynthia's average speed. (Round your answer to the nearest tenth.)

  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.