Ratios, Rates and Percents Lesson 11 Ratios, Rates and Percents Motion Rates

Warm-Up Stan runs at a rate of 7 miles in 1 hour. Pat runs at a rate of 9 miles in 1.5 hours. Which person runs at a faster rate? A local berry farm charges $3.00 for 4 pounds of berries. How much will it cost to buy 12 pounds of berries at the local farm?

Target: Solve problems, compare and convert motion rates.

Vocabulary Motion Rate: A rate that compares distance to time. Rate Conversion: A process of changing at least one unit of measurement in a rate to a different unit of measurement.

Example 1 Oksana’s family traveled on a highway through central Oregon at a rate of 60 miles per hour. Her family traveled at this rate for 2.5 hours. How far did they drive? Locate the unit rate. 60 miles per hour Multiply by 2.5 hours. 60 × 2.5 = 150 Oksana’s family traveled 150 miles in 2.5 hours.

Example 2 Find Wayne’s unit rate of speed. Wayne and Marla each left home on their bikes. They were meeting at the library, which is exactly the same distance from each of their homes. Wayne traveled at a rate of 20 miles every 2 hours. Marla traveled at a rate of 6 miles every 0.5 hour. They left at the same time. Who arrived at the library first? Find Wayne’s unit rate of speed. Find Marla’s unit rate of speed. Marla rode faster, so she arrived at the library first.

Converting Rates Write the rate as a fraction. Identify the units you want in the answer. Multiply the original rate by a conversion rate using equivalent measurements. Make sure the unwanted units cancel to get the answer.

Example 3 Convert 4 miles per hour to feet per hour. Write the rate as fraction. Identify units in answer. Fill in conversion rate. Multiply. 4 miles per hour = 21,120 feet per hour

Example 4 Convert 3 feet per minute to feet per hour. Write the rate as fraction. Identify units in answer. Fill in conversion rate. Multiply. 3 feet per minute = 180 feet per hour

Exit Problems Michael rode his bike at a rate of 10 miles per hour. If he rode at this rate for 3 hours, how far did he ride? Identify the faster rate: or Convert 3 miles per hour to feet per hour.

Communication Prompt Suppose you walk to school at a rate of 4 miles per hour. How can you convert this rate to feet per hour? OR Think of as many conversion rates as possible. Write the conversion rates in a list.