Ruth sets out to visit her friend ward, who lives 20 mi north and 100 mi east of her. she starts by driving east, but after 70 mi she comes to a detour that takes her 15 mi south before going east again. she then drives east for 8 mi and runs out of gas, so ward flies there in his small plane to get her.

Solution:Distance between Ruth House and Ruth Friend House =20 Meter north and 100 meter east of RuthNow , Ruth Starts Driving, but after 70 mi she comes to a detour that takes her 15 mi south before going east again. she then drives east for 8 mi and runs out of gas.The Diagram of Ruth Driving is depicted below.Now , when ward flies in small plane to get Ruth,So, Distance between Ruth and Ward , when Ruth is at Point S=SMIn Right Δ SVM, By Using Pythagoras theoremSM²=SV² + VM²DT=VS=15 mVM=100 - (70+8)      = 100 -78      =22 meterSM²=(15)² + (22)²        = 225 + 484        = 709[tex]SM=\sqrt{709}=26.62[/tex]So, Ward has to travel 26.62 miles east north to reach Ruth.