Answer to Question #330842 in Trigonometry for Shang

Question

Solve each of the following problems. Follow Polya's four stages of problem solving in your solution.

6. Your house is two km due north of a river that runs east-west. Your grandmother's house is located 12 km west and 1 km north of your house. Every day, you go from your house to Grandma's, but first visit the stream (to get fresh water for Grandma). What is the length of the route with minimum distance?

7. If 10 cows can eat 10 bags of grain in 10 days, how many days will it take for one Icow to eat one bag of grain?

Answer 1

6.

Finding the shortest way to Grandma is the same as finding the shortest way to Grandma', which is simply a line. Then the route is:

$R = \sqrt{5^2+12^2}=13\ miles$

Answer: 13 miles.

7.

If 10 cows can eat 10 bags of grain in 10 days, then 9 cows eat 9 bags in 10 days, 8 cows eat 8 bags in 10 days, ..., finally, 1 cow eats 1 bag in 10 days.

Answer: 10 days.