1. ALGEBRA READINESS LESSON 6-4 Warm Up Lesson 6-4 Warm-Up

2. ALGEBRA READINESS LESSON 6-4 Warm Up Lesson 6-4 Warm-Up

3. ALGEBRA READINESS “Application of Rates” (6-5) How do you find the total distance if you are given time traveled at two or more speeds? ” work? By dimensional analysis, the product of time and speed (rate) is total distance traveled, or d = rt. Proof: hours = = = miles Sometimes, you have to two or more times and rates in a problem. In these cases, you will need to find the distances at each rate and add them together. Example: It takes you 1.25 hours at 7 mi./hr. to bike from your house to the lake. Then, it takes you 1 hour to bike to the store at 9 mi./hr. What is the total distance traveled from your home to the store? Find the distance for each part of the trip. miles hour hours 1 miles hour miles 1 You bike a total of 17.75 mi.

4. ALGEBRA READINESS A bus is driven from the center of a city to its first stop. The trip takes 0.25 h at 15 mi/h. The bus then continues on the highway to a park-and-ride station. The trip takes 0.50 h at a speed of 56 mi/h. What is the total distance traveled by the bus? distance to stop = rate to stop time to stop mi h = 15 0.25 h = 3.75 mi distance to station = rate to station time to station mi h = 15 0.50 h = 28 mi The bus travels a total of 31.75 miles. total distance = 3.75 mi + 28 mi Add the two distances. = 31.75 mi Simplify. Applications of Rates LESSON 6-4 Additional Examples

5. ALGEBRA READINESS How do you find the average speed? s” work? Since d = rt, where d = distance, r = rate (speed), and t = time: average rate (speed) = distance / time Proof: If we divide both sides of d = rt by t to isolate r: = r or r = (Example: ) Example: A car travels 35 mi./hr. for 1 hour. It then travels 50 mi./hr. for 1.5 hours. What is the cars average speed over the total distance? d td t d td t t tt t miles hours “Application of Rates” (6-5)

6. ALGEBRA READINESS A speed skater travels 8 m/s for 30 s, and then travels 6 m/s for 18 s. What is the skater’s average speed over the total distance? m s total distance = 8 30 s + 6 18 s = 348 m m s total time = 30 s + 18 s = 48 s average speed = total distance total time Average speed is the total distance divided by the total time. = 348 m 48 s Substitute the values for total time and total distance. = 7.25 m s Simplify. The skater’s average speed is 7.25 m/s. Applications of Rates LESSON 6-4 Additional Examples

7. ALGEBRA READINESS At a poster store, the shipping cost of a poster varies directly with its width. It costs $12 to ship a poster that has a width of 16 inches. What is the shipping cost of a poster that has a width of 20 inches? $12 16 in. = 0.75 $ in. Find the unit rate. 20 0.75 = 15 Multiply the width by the unit rate. A 20-inch poster will cost $15 to ship. Check for Reasonableness Use dimensional analysis to check the units: in. = $. The question asked for cost, so the answer is reasonable. $ in Applications of Rates LESSON 6-4 Additional Examples

8. ALGEBRA READINESS Find each total distance. 55 mi/h for 1.5 hours and 60 mi/h for 0.75 hours 2. 8 meters per second for 2.5 seconds and 6 meters per second for 1.8 seconds The quantities vary directly. Find each missing quantity. 3. 53 miles : 2 gallons; ? miles : 5 gallons 4. 16 feet : 2.5 seconds; ? feet : 5.6 seconds 1. 127.5 miles 30.8 meters 132.5 35.84 Applications of Rates LESSON 6-4 Lesson Quiz