SAT Math: Ratios, Rates, and Unit Conversion Practice Questions
Track units through proportional models, weighted rates, scale drawings, and conversions of length, area, and volume. Try each original question before checking its worked explanation. This focused practice is free and requires no account.
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1. A pump moves 42 liters of water in 3.5 minutes at a constant rate. How many liters does it move in 8 minutes?
Explanation. The unit rate is 42/3.5 = 12 liters per minute. In 8 minutes the pump moves 12(8) = 96 liters.
2. A map uses a scale of 1 centimeter to 4 kilometers. Two towns are 6.5 centimeters apart on the map. What is their represented distance in kilometers?
Explanation. Multiply the map distance by 4 kilometers per centimeter: 6.5(4) = 26 kilometers. The centimeter units cancel.
3. A tank contains 2.4 cubic meters of water. Given 1 cubic meter = 1,000 liters, how many liters does it contain?
Explanation. Use the stated volume conversion directly: 2.4 cubic meters times 1,000 liters per cubic meter = 2,400 liters.
4. A cyclist rides 30 kilometers in 1 hour and then 30 kilometers in 2 hours. What is the average speed for the whole trip, in kilometers per hour?
Explanation. Average speed is total distance divided by total time: (30 + 30)/(1 + 2) = 60/3 = 20 kilometers per hour. The two speeds last for different durations, so their simple average is not appropriate.
5. A rectangular sheet has area 450 square centimeters. Given 10 millimeters = 1 centimeter, what is its area in square millimeters?
Explanation. Each centimeter of length equals 10 millimeters, so a square centimeter equals 10^2 = 100 square millimeters. The area is 450(100) = 45,000 square millimeters.
6. Blue and white paint are mixed in a volume ratio of 3:5. A batch contains 24 liters total. How many liters of white paint are in the batch?
Explanation. There are 3 + 5 = 8 equal ratio parts in total. Each part is 24/8 = 3 liters. White paint uses 5 parts, or 15 liters.
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FAQ
How do I check a conversion?
Write the conversion as a fraction so the original unit cancels. Square or cube a length conversion when converting area or volume.
What is average speed?
Average speed is the total distance traveled divided by the total elapsed time. It need not equal the average of the individual segment speeds.