Rates, Work & Speed • Topic 1 of 4

Unit Rates & Unit Conversion

A unit rate expresses "how much per one" — 45 miles per hour, $2.40 per pound, 12 pages per minute — and you get it by dividing the amount by the number of units. Unit rates make comparisons fair: to decide which package is the better buy, reduce each to a price per ounce and compare. Unit conversion is the same skill run in reverse: multiply by a conversion factor written as a fraction equal to 1, arranged so the unwanted unit cancels. To turn 90 km/h into metres per second, multiply by 1000 m / 1 km and by 1 h / 3600 s, and the km and h cancel to leave 25 m/s. The GRE mixes units on purpose — a speed in km/h with a time in minutes — so the reliable habit is to convert everything to consistent units before you compute. Because the calculator is basic, keep the conversion factors as simple fractions and cancel before multiplying.

✅ Solved examples

1. A printer produces 320 pages in 8 minutes. Find its rate in pages per minute.
Unit rate = 320 / 8 = 40 pages per minute.
2. Which is cheaper per litre: 3 L for $8.40 or 5 L for $13.50?
8.40/3 = $2.80 per L; 13.50/5 = $2.70 per L. The 5-litre pack is cheaper.
3. Convert 72 km/h into metres per second.
72 × (1000 m / 3600 s) = 72000/3600 = 20 m/s. (Shortcut: km/h ÷ 3.6 = m/s.)
4. A car uses 6 litres of fuel per 100 km. How many litres for a 250 km trip?
Rate = 6 L per 100 km = 0.06 L/km. For 250 km: 250 × 0.06 = 15 litres.

✏️ Practice — try these, take hints as needed

1. A machine fills 450 bottles in 15 minutes. Find the rate in bottles per minute.
Divide amount by units.
450 / 15.
Simplify.
30 bottles per minute
2. Which is the better value: 4 kg for $11.60 or 6 kg for $16.80?
Find price per kg for each.
11.60/4 = 2.90; 16.80/6 = 2.80.
Lower per-kg wins.
6 kg pack ($2.80/kg)
3. Convert 15 m/s to km/h.
m/s × 3.6 = km/h.
15 × 3.6.
Or use 3600 s and 1000 m.
54 km/h
4. A tap delivers 18 litres per minute. How many litres in 40 seconds?
Convert the rate to per second.
18/60 = 0.3 L/s.
0.3 × 40.
12 litres
5. A worker earns $153 for a 9-hour shift. What is the hourly rate, and the pay for 5 hours?
Hourly = 153/9.
= $17 per hour.
5 × 17.
$17/h; $85

📝 Topic test — 8 questions

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