Answer:
The rate is 13 miles per hour
Step-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
