SAT-Style: Unit Rate and Conversion

SAT Math · Axiom Academy

SAT-Style Unit Rate & Conversion Multi-step dimensional analysis problems Problem 1: Speed Conversion - Miles/Hour to Feet/Second A car travels at a constant speed of 45 miles per hour. How many feet per second is this? (Hint: 5,280 feet = 1 mile, 3,600 seconds = 1 hour) Step 1: Set Up the Starting Ratio We begin with 45 miles per hour: Multiply by the conversion factor for miles to feet. We want feet in the numerator and miles in the denominator so they cancel: The "miles" unit cancels, leaving us with feet in the numerator: Step 3: Convert Hours to Seconds Multiply by the conversion factor for hours to seconds. We want seconds in the denominator and hours in the numerator so they cancel: The "hour" units cancel, leaving feet per second: 45 miles per hour = 66 feet per second Problem 2: Compound Rate Conversion A factory produces 240 widgets per 8-hour shift. How many widgets does the factory produce per minute? Express your answer as a rate with units. Step 1: Find the Unit Rate (Widgets per Hour) First, convert the production rate to widgets per hour: Step 2: Convert Hours to Minutes Now convert from per hour to per minute. Since 1 hour = 60 minutes: Does 0.5 widgets/minute make sense? 0.5 widgets/minute × 60 minutes/hour = 30 widgets/hour ✓ 30 widgets/hour × 8 hours = 240 widgets ✓ Problem 3: Real-World Multi-Step Problem

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