Jim lives three miles east of State College. At noon, he leaves his house and begins to walk due east at a constant speed of 2 miles per hour. Annie lives four miles north of State College. At noon, she leaves her house and begins to bicycle due north at a constant speed of 8 miles per hour. Calculate the rate at which the distance between the two people is changing when it is 1 p.m.

Answer:The rate is 13 miles per hourStep-by-step explanation:* Lets explain how to solve the problem- Jim lives three miles east of State College- At noon, he leaves his house and begins to walk due east at a  constant speed of 2 miles per hour- Annie lives four miles north of State College- At noon, she leaves her house and begins to bicycle due north at a  constant speed of 8 miles per hour- The east is perpendicular to the north* Lets solve the problem∵ At noon means 12 p.m∵ They moved till 1 p.m∵ Jim walked for 1 hour and Annie bicycled for 1 hour∵ The rate of Jim is 2 miles per hour∵ The rate of Annie is 8 miles per hour- The distance = rate × time∴ Jim walked = 2 × 1 = 2 miles∴ Annie bicycled = 8 × 1 = 8 miles- Lets calculate the distance of Jim from the State College till his  position at 1 p.m∵ Jim lives three miles east of State College∴ His distance at 1 p.m = 3 + 2 = 5 miles east- Lats calculate the distance of Annie from the State College till her  position at 1 p.m∵ Annie lives four miles north of State College∴ Her distance at 1 p.m = 4 + 8 = 12 miles North- Lets find the distance between them at 1 p.m∵ The north ⊥ east- Use Pythagoras Theorem to find the distance∴ The distance = √(5² + 12)² = √(25 + 144) = √169 = 13 miles- The rate = distance/time∵ The distance between them is 13 miles in 1 hour∴ The rate = 13/1 = 13 miles per hour* The rate is 13 miles per hour