Ratios and Proportions • Topic 7 of 7

Unit Rates

A unit rate expresses how much of one quantity corresponds to exactly one of another — miles per hour, dollars per item, words per minute. You find it by dividing the first quantity by the number of units of the second. Unit rates make comparisons fair: to find the better buy, compare price per unit, not total price. The SAT uses unit rates in speed, pricing, density and productivity problems, and the built-in calculator makes the division quick. Always label the unit (per hour, per gram) so you set up the division the right way round.

✅ Solved examples

1. A car travels 180 miles in 3 hours. What is its speed in miles per hour?
180 ÷ 3 = 60 miles per hour.
2. 8 pens cost $6. What is the cost per pen?
6 ÷ 8 = $0.75 per pen.
3. Which is the better buy: 12 oz for $3 or 20 oz for $4?
Unit prices: 3/12 = $0.25/oz and 4/20 = $0.20/oz. The 20 oz pack is cheaper per ounce.
4. A printer prints 90 pages in 5 minutes. What is its rate per minute?
90 ÷ 5 = 18 pages per minute.

✏️ Practice — try these, take hints as needed

1. A runner covers 100 metres in 20 seconds. What is the speed in metres per second?
Divide distance by time.
100 ÷ 20.
Compute.
5 m/s.
2. 5 kg of rice costs $20. What is the price per kg?
Divide cost by weight.
20 ÷ 5.
Compute.
$4 per kg.
3. Which is cheaper per litre: 4 L for $10 or 6 L for $13.50?
Find each price per litre.
10/4 = $2.50 and 13.50/6 = $2.25.
Smaller is cheaper.
6 L for $13.50 ($2.25/L).
4. A typist types 240 words in 4 minutes. What is the rate per minute?
Divide words by minutes.
240 ÷ 4.
Compute.
60 words per minute.
5. A car uses 12 litres of fuel for 150 km. What is the rate in km per litre?
Divide distance by fuel.
150 ÷ 12.
Compute.
12.5 km per litre.

📝 Topic test — 8 questions

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