Problem of the Week 05-23-16

Lower Elementary:
Question: A starship begins its mission with 100 fuel units. It uses 25 fuel units on the first leg of its mission, 50 fuel units on the second leg of its mission, and 5 units on the last leg of its mission. How many fuel units does the starship have now?
Answer:  20 Fuel Units
Solution:  After the first leg of the trip, the starship has 100 – 25 = 75 fuel units left. After the second leg of the trip, the starship has 75 – 50 = 25 fuel units left. After the last leg, it has 25 – 5 = 20 fuel units left.

Upper Elementary:
Question: A fairy has a wingspan of 17 centimeters. That’s the length of both wings completely outstretched. If 5 fairies line up wingtip-to-wingtip, how long would the line of fairies be?
Answer:  85 centimeters
Solution:  To find the length of a line of 5 fairies whose wingspans are each 17 centimeters, we have to multiply 17 by 5. One way to do this is to multiply the wingspan by 10, then take half of it. 17 × 10 = 170. Half of 170 = 85 centimeters.

Middle School:
Question: When it isn’t windy outside, a superhero can fly at 100 miles per hour. Today, the superhero is flying against the wind, which slows him down by 15 miles per hour. How far can the superhero fly in 45 minutes?
Answer:  633/4 miles
Solution:  The superhero can fly 100 – 15 = 85 miles per hour against the wind. In 45 minutes, or 3/4 of an hour, he can fly 3/4 of 85 miles. 1/4 of 85 is 211/4, so 3/4 of 85 is 211/4 × 3 = 633/4.

Algebra and Up:
Question: The average speed of an object in motion can be calculated by dividing the distance traveled by the time it takes to get there. A dragon located 39 miles North and 52 miles West of a castle takes flight, flies for 40 minutes, and lands 27 miles South and 36 miles East of the castle. What was the dragon’s average speed in miles per hour?
Answer:  165 miles per hour
Solution:  The dragon flies a total of 39 + 27 = 66 miles South and 52 + 36 = 88 miles East. These distances form the legs of a right triangle, and the dragon flies on the path of its hypotenuse.  We can solve for the length of the hypotenuse with the Pythagorean theorem, or we can observe that 66 and 88 are multiples of 3 and 4, so this must be a 3-4-5 triangle whose hypotenuse must be 110 miles. If the dragon flies that distance in 40 minutes, then we can multiply it by 11/2 to find the distance it flies in an hour. 110 × 11/2 = 165 miles per hour.