You are 2 km from the launch pad, watching a mighty rocket climb skyward, under the fearless command of the intrepid Captain Knight. Your first observation gives an angle of elevation of 21 degrees. Five seconds later, the angle increases to 35 degrees. What was the rocket’s average speed during the five-second interval?
True Statements on Card
Here is a card with the four statements that you see, and no others. Assume that each statement on the card is either true or false; then find and identify each false statement. (Refer to them as a, b, c, d if you want, to speed things up.)
On this card exactly two statements are true.
On this card exactly three statements are true.
On this card exactly four statements are true.
Denmark is a major manufacturer of energy-producing wind turbines. Suppose both the following statements are true:
1. Some wind turbines in Ohio are not from Denmark, but are American-built.
2. All of the wind turbines in Lorain County are indeed from Denmark.
From these two statements, which of the following can be concluded?
- Some American-built wind turbines are in Lorain County.
- All Lorain county wind turbines are not American-built.
- Some American-built wind turbines are not in Lorain County.
- No Lorain County wind turbine is American-built.
- Some wind turbines in Ohio, but not in Lorain County, were built in Denmark.
Clock Hands Overlap After Noon
At what time, exactly, do the two hands of a clock overlap for the first time after 12:00 noon?
Area Ratio, Circles and Square 1
Find the ratio of the area of the circle circumscribed about a given square to the area of the circle inscribed in that square.
Given: lines y = 3x + 1, y = -2x + 5, and a third line L1: y = mx + c with m > 0 and c a constant. L1 moves parallel to itself intersecting the two given lines in points P1 and P2 respectively. The locus of mid-points of segment P1P2 is line L2. Find the slope of L1 so that L2 has a slope that is undefined.
Present and Future Ages 2
Sosthenes is three times as old as Benoni. Five years from now the sum of their ages will be 34 years. What are their present ages?
Driving to Atlanta
Manzy’s car, that he had in the 1980’s, had a 24-gallon gas tank. When he started driving one morning with a full tank, heading for Atlanta, the odometer read 3208 miles. He drove for most of the day, having stopped at lunch to buy 5 gallons of gas. The gas gauge said exactly � of a tank at the point where the odometer read exactly 3668. He still had 130 miles of driving to do to get to Atlanta. Back then, gas cost only $1.09 per gallon, and he had only $2.00 left on him and no credit cards. Did he make it into the city? (Give all details.)
Driving to See Grandmother
Kim drove 84 miles to see her grandmother. Nine miles of the trip were inside the city limits. Her average speed outside the city was 12 mph faster than inside the city. The whole trip took 3 hours. How fast did Kim go while inside the city?
Glenice has two candles of the same length, but made of different materials so that one lasts 4 hours and the other lasts 3 (each burns at a constant rate). At what time should Glenice light both candles so that at 4:00 pm one stub is exactly twice the length of the other?