From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

Sample Problem Sets

Unit Conversion

1. Jonae is 5 feet tall. How tall is Jonae in inches?
2. Kevin has television that is 24 inches tall. If Kevin set the television on a stand that is one foot tall, how far from the floor will the top of the television be in feet, and in cm?
3. A football field is 100 yards from end to end. What is the length of a football field in feet?
4. Coby started his homework at 1:50 p.m. and finished his homework 96 minutes later. Coby had band practice at 4:00 p.m. How much time did Coby have between finishing his homework and the beginning of band practice?
5. How many seconds did Coby have before band practice?
6. Daquan and Richard each ran 30 minutes on a treadmill. Richard’s treadmill said he had run 10,000 feet. Daquan’s treadmill said he had run for 2 miles. Who ran farther, and how much farther?
7. How many inches farther?
8. How many centimeters farther?
9. Ballou’s science group built a robot that carries a cube with 12 cm long edges. Anacostia’s group built a robot that carries a cube with 4 cm long edges. How many times larger is the volume of the larger cube than the smaller one?
10. Suppose your weight on Earth is 166 pounds. The force of gravity on Mars is only 1/3 of the force of gravity on Earth. If you go to Mars and stand on a scale that measures weight in pounds, what would it record as your weight?
11. Meyers’ laptop weighs 6.3 pounds. What is the weight of his laptop in ounces? Your answer should have 4 significant digits.
12. A crayon has a mass of 25 grams. How many crayons can be made with 25 kilograms of colored wax? We will ignore accuracy issues here.
13. Brianna took 12 minutes 40 seconds to type a 500-word essay. Kianna took 15 minutes 12 seconds to type the same essay. How much longer did Kianna take to type the essay than Brianna?

Displacement and Total Distance Travelled

1. An Escalade navigates the neighborhood on MLK Avenue by traveling East for a distance of 5 km, turns around and goes West for 2 km and finally turns around again and heads East for 4 km.
   1. What is the total distance traveled?
   2. What is the displacement?
2. 
   1. Calculate the distance an object travels starting from position 1 to position 4, and then reversing direction and ending at position 2.
   2. Calculate the displacement of an object that starts at position 1, travels to position 5, then reverses to position 4.
   3. Calculate the distance an object travels, starting from position -2, moving to position 3, and then reversing direction to 0.
3. If you run exactly four times around a quarter-mile track, what is your displacement? Why? Calculate the total distance traveled.
4. An object moves along the grid through the points A, B, C, D, and E as shown below.
   1. Find the distance traveled by the moving object.
   2. Find the magnitude of the displacement of the object

Rates of Motion

1. How long will it take a bus traveling 65 km/hr to travel 260 km?
2. How fast, in miles per hour, must a car travel to go 600 miles in 15 hours?
3. Grace is driving her sports car at 20 m/s when a ball rolls out into the street in front of her. Grace slams on the brakes slows her speed to half of her initial speed. What is Grace’s average speed in miles per hour? Grace comes to a complete stop in 3.0 seconds, her average breaking speed is half her initial speed (20 m/s), calculate the total distance, in meters, Grace would traveled while braking.
4. Jay-Juan and Romello live 5 miles apart. The both start walking toward each other at noon, one at a rate of 3 mph, and the other at 4 mph. After how many hours will they meet? To the nearest minute, how long will they walk until they meet?
5. A car travels 7 hours from Washington, DC to New York. Use the table to answer the following questions.
   1. Calculate the average speed of the car
   2. According to the table, is the car moving at a constant speed in its first seven hours of travel? Support you answer.
   3. If the car travels in constant motion, how long would it take to travel 210 miles?