Math Problem Monday - June 1st, 2020 | Mathnasium Livermore, CA

Lower Elementary
Question: A small dog’s heart beats 120 times a minute. How many times will the dog’s heart beat in 5 minutes?
Answer: 600 times
Solution: In order to solve this problem we find what 120 five times is.

120 + 120 + 120 + 120 + 120 = 600

This problem can also be solved using multiplication. Since 120 = 100 + 20.

120 x 5 = 100 x 5 + 20 x 5 = 500 + 100 = 600

Upper Elementary
Question: Frank can throw a baseball a fourth of the distance that Eric can throw. Pete can throw a baseball twice as far as Eric. If Pete can throw a baseball 120 feet, how far can Frank throw a baseball?
Answer: 15 feet
Solution: We can solve this problem by working backwards from Pete to Frank.

If Pete can throw a baseball twice as far as Eric, then to find how far Eric can throw take half of 120.

Half of 120 = 60. Eric can throw the ball 60 feet.

Since Frank can throw a baseball a fourth as far as Eric, we can find how far Frank throws the ball by taking a fourth of 60 (half of half of 60).

Half of 60 = 30 and half of 30 = 15. Frank can throw the ball 15 feet.

Middle School
Question: If 18 is 20% of a number, what is 50% of the same number?
Answer: 45
Solution: This problem can be done mentally. Since 20 + 20 + 10 = 50, we can find 50% of the number by adding 20% of the number plus 20% of the number plus 10% of the number, which is half of 18.

20% of x + 20% of x + 10% of x = 18 + 18 + 9 = 45

This problem can also be solved by using proportions. Let x be the number we are looking for.

18/x =20/100
20x = 18000
x = 90

That means 18 is 20% of 90.

50% of 90 is half of it, 45.

Algebra and Up
Question: The SR-71 Blackbird was used during the cold war as a spy plane. With a maximum speed of Mach 3.5, it is the fastest manned aircraft in the world. A Mach number is defined as the ratio of the speed of an aircraft to the speed of sound (about 761 mph). How many miles does the SR-71 travel in 5 minutes?
Answer: 221.95 miles
Note: In order to solve this problem we need to first find how fast Mach 3.5 is in miles per hour. We do this by multiplying 3.5 by the speed of sound, 761 mph.

3.5 ● 761 mph = 3 ● 761 + half of 761 = 2283 + 350 +30 + .5 = 2663.5 mph

Now we find, at that speed, how many miles the SR-71 travels in a 1 minute.

2663.5 miles/hours ● (1 hr / 60 min) = 44.39 miles per minute.

Finally multiply the result by 5. 44.39 • 5 = 221.95 miles.