distance problem

Question

Steve and Elsie are camping in the desert, but have decided to part ways. Steve heads north, at 7 AM, and walks steadily at 2 miles per hour. Elsie sleeps in, and starts walking west at 2.5 miles per hour starting at 9 AM.

When will the distance between them be 30 miles? (Round your answer to the nearest minute.)

Answer 1

Our walkers are making a right angle. The distance between them is the hypotenuse.

 

(2t)² + (2.5(t - 2))² = 30²

4t² + (2.5t - 5)² = 900

4t² + 6.25t² - 25t + 25 = 900

2.25t² - 25t - 875 = 0

 

Solve for t, then add to 7:00 for your time.