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News from Mathnasium of Coral Springs / Parkland

Problem of the Week 12-12-16

Dec 12, 2016

Lower Elementary:

Question: Apollo 17 was the most recent manned spacecraft to go to the moon. It took 110 hours to get there. How many full days did it take the astronauts to get to the moon?

Answer: 4 full days

Solution: There are 24 hours in a day, so we can solve this problem by counting up to 110 by 24. One day is 24 hours, two days is 48, three is 72, four is 96, and 5 is 120. 120 is too many, so we know that it took 4 full days to get to the moon. Since 110 hours is 14 more hours than 96 hours, it took 4 days and 14 hours.

Upper Elementary:

Question: The Earth’s orbit about the Sun is approximately 600 million miles. That’s how far it travels in a full year. How far does the Earth travel about the Sun in 3 months?

Answer: 150 million miles

Solution: Since 3 months is a fourth of a full year, that means that the Earth travels a fourth of its orbital path. That’s 600 million miles ÷ 4 = 150 million miles.

Middle School:

Question: A space shuttle has 1 large fuel tank and 3 small fuel tanks. The tanks are filled with 600 tons of fuel in total. The large fuel tank is completely filled with 400 tons of fuel, and the rest of the fuel fills 21/2 small tanks. How much does each small tank hold when full?

Answer: 80 tons of fuel.

Solution: Since 400 of the 600 tons of fuel are in the large tank, there are 600 – 400 = 200 in the small tanks. Because 21/2—or 5/2—of the tanks can be filled with 200 tons of fuel, we can reason that each of the 5 half-tanks can be filled with 200 ÷ 5 = 40 tons. That means that each small tank can hold 40 tons × 2 = 80 tons of fuel.

Algebra and Up:

Question: The volume of a sphere is equal to 4/3πr3, in which r is the radius of the sphere. The radius of the Earth is 4,000 miles. The radius of the moon is 1,000 miles. How many cubic miles greater in volume is the Earth than the moon?

(Round π and all other irrational numbers to 3 figures.)

Answer: 263,810,000,000 cubic miles

Solution: The volume of the Earth is . . .

4/3 × 3.14 × 4,0003 ≈ 268,000,000,000 cubic miles.

The volume of the moon is . . .

4/3 × 3.14 × 1,0003 ≈ 4,190,000,000 cubic miles.

The difference is therefore approximately 263,810,000,000 cubic miles.