Problem of the Week October 30

Lower Elementary:
Question: What time is it if the minute hand of a clock is pointed at the second small mark past the 2, the hour hand is pointed between the 5 and 6, and it is the afternoon?
 

Upper Elementary:
Question: What number is exactly between one-seventh and two-sevenths?
 

Middle School:
Question: On a map, an inch represents a quarter of a mile. How many miles apart are a bank and a grocery store in real life if they are 2¹/₂ inches apart on the map?
 

Algebra and Up:
Question: What is the area of a triangle whose vertices lie on the points (1, 3), (22, 3), and (7, 11)? Draw the triangle on a coordinate plane to help you solve the problem.
 

WARNING: ANSWERS AHEAD!!!

Lower Elementary:
Question: What time is it if the minute hand of a clock is pointed at the second small mark past the 2, the hour hand is pointed between the 5 and 6, and it is the afternoon?
Answer: 5:12 PM
Solution: Each number marked on the clock represents 5 minutes, and 5 minutes two times is 10 minutes. Two marks past 10 minutes is 10 + 2 = 12 minutes. Since the hour hand has passed the 5 but hasn’t yet passed the 6, it must be 5:12 PM.

Upper Elementary:
Question: What number is exactly between one-seventh and two-sevenths?
Answer: Three-fourteenths
Solution: There aren’t any whole sevenths between one-seventh and two-seventh, so let’s turn them into fourteenths: ¹/₇ = ²/₁₄, and ²/₇ = ⁴/₁₄. So, since 3 is exactly between 2 and 4, three-fourteenths must be the number that is exactly between one-seventh and two-sevenths.

Middle School:
Question: On a map, an inch represents a quarter of a mile. How many miles apart are a bank and a grocery store in real life if they are 2¹/₂ inches apart on the map?
Answer: ⁵/₈ of a mile
Solution: Since each inch represents a quarter mile, 2 inches represents ¹/₄ × 2 = ¹/₂ a mile. Half of an inch represents half of a quarter mile, which is ¹/₄× ¹/₂ = ¹/₈ of a mile. So, 2¹/₂ inches represents ¹/₂ + ¹/₈ = ⁵/₈ of a mile.

Algebra and Up:
Question: What is the area of a triangle whose vertices lie on the points (1, 3), (22, 3), and (7, 11)? Draw the triangle on a coordinate plane to help you solve the problem.
Answer: 84 square units
Solution: The line segment that connects (1, 3) and (22, 3) is the base of the triangle, so its base is 22 – 1 = 21 units. The base of the triangle lies on the line y = 3, and the highest point of the triangle lies on the line y = 11, so its height is 11 – 3 = 8. The area of a triangle is half of its base times its height, so the triangle is ¹/₂ × 21 × 8 = 84 square units.