Speed, Distance, and Unit Rates Quiz

Study Notes

Speed: A measure of how fast an object moves, typically expressed in units like miles per hour (mph) or meters per second (m/s).
Distance: The total length of the path traveled by an object.
Formula:
- Speed = Distance / Time
- Rearranged: Distance = Speed × Time, Time = Distance / Speed
Example Problem: If a car travels 120 miles in 2 hours, speed = 120 miles / 2 hours = 60 mph.
Units: Ensure consistent units for calculations (e.g., converting hours to minutes).

Definition: A unit rate compares a quantity to one unit of another quantity (e.g., price per item, miles per hour).
Calculation:
- Unit Rate = Total Quantity / Number of Units
Example: If a car uses 15 gallons of gas to travel 300 miles, the unit rate is 300 miles / 15 gallons = 20 miles per gallon.
Applications: Useful for comparing costs, speeds, and efficiencies.

Definition of Ratio: A comparison of two quantities, expressing how much of one exists relative to another (e.g., 2:3).
Types of Ratios:
- Part-to-Part: Compares different parts (e.g. 2 apples to 3 oranges).
- Part-to-Whole: Compares a part to the total (e.g. 2 apples out of 5 fruits).
Solving Ratio Problems:
- Set up a proportion if needed: a/b = c/d.
- Cross-multiply to solve for unknowns.
Example Problem:
- If the ratio of boys to girls in a class is 3:4 and there are 12 boys, how many girls are there?
- Set up the ratio: 3/4 = 12/x; cross-multiply: 3x = 48; x = 16 girls.

Speed measures the rate at which an object moves and is commonly expressed in miles per hour (mph) or meters per second (m/s).
Distance refers to the total length of the path an object travels.
Key Formulas:
- Speed formula: Speed = Distance / Time
- Rearranged: Distance = Speed × Time, Time = Distance / Speed
Example Calculation: If a car covers 120 miles in 2 hours, then the speed is calculated as 60 mph.
Unit Consistency: When performing calculations, ensure that units are consistent, such as converting hours to minutes for accuracy.

Unit Rate compares a quantity to one unit of another, illustrating relationships like cost per item or speed.
Calculation Method: Unit Rate = Total Quantity / Number of Units.
Practical Example: A car that uses 15 gallons of gas for 300 miles travels at a unit rate of 20 miles per gallon.
Real-World Applications: Unit rates help in comparing efficiencies, costs, and speeds effectively.

Definition of Ratio: A ratio indicates the relationship between two quantities, expressed in a format like 2:3.
Types:
- Part-to-Part: Compares different components (e.g., 2 apples to 3 oranges).
- Part-to-Whole: Compares a part to the total quantity (e.g., 2 apples out of 5 total fruits).
Solving Ratios:
- Set up a proportion if necessary: a/b = c/d.
- Use cross-multiplication to find unknown quantities.
Example Ratio Problem: In a class where the ratio of boys to girls is 3:4 and there are 12 boys, 16 girls can be determined by setting up the proportion and solving it (3/4 = 12/x).