**Let helicopter start at A, travel east at 45 mi/hr for time t1 hrs till B. It then turns north and travels at 40 mi/hr for t2 hrs till C. **

**Now AC = 150 mi** and ABC is a right angle triangle.

**t1 + t2 = 5 hrs**

**Displacement is AC = 150 miles**

**AB² + BC² = AC² **

**(45 t1)² + (40 t2)² = 150² simplify by canceling 5²**

**81 t1² + 64 t2² = 900**

**81 t1² + 64 (5 - t1)² = 900**

**145 t1² - 640 t1 + 700 = 0 29 t1² - 128 t1 +140 = 0**

**Δ = 128² - 4 * 29 * 140 = 144**

**t1 = (128 +- 15) / 2*29 = 1.95 hr or 2.46 hr**

**t2 = 3.05 hrs or 2.54 hrs**

**t1, t2 = (1.95 hrs, 3.05 hrs) or ( 2.46 hrs , 2.54 hrs)**

**Either of the two combinations you get to C. Both sets are correct.**