Compound Measures Flashcards

All 7 cards in this deck

What is a compound measure?

A measure made from two other units divided by one another.
e.g. speed (distance per unit time), density, pressure, rate of pay.

What does 'time and a half' mean for an hourly rate of pay?

Each overtime hour is paid at $1.5 \times$ the normal hourly rate.
e.g. £12 per hour becomes £18 per hour.

What are the steps to work out a day's pay when overtime is paid?

e.g. 10 hours worked, £12 per hour, overtime at $1\frac{1}{4}$ times after 8 hours

1. Pay for normal hours: $12 \times 8 = £96$
2. Overtime hours and rate: $10 - 8 = 2$ hours at $1.25 \times 12 = £15$
3. Add: $96 + 2 \times 15 = £126$

What is the formula for flow rate?

Flow rate = volume $\div$ time.
e.g. measured in litres per minute or cm$^3$ per second.

What must you check about the units before using a compound measure formula?

e.g. mass 12.5 kg with density in g/cm³

The units must match the formula's units — convert first: $12.5$ kg $= 12\,500$ g, giving a volume in cm$^3$.

What are the steps to find the density of a drink made by mixing two liquids of different densities?

e.g. 20 cm³ of syrup at 1.4 g/cm³ mixed with 80 cm³ of water at 1 g/cm³

1. Mass of each $=$ density $\times$ volume: $20 \times 1.4 = 28$ g and $80 \times 1 = 80$ g
2. Add for the totals: mass $= 108$ g, volume $= 100$ cm³
3. Density $=$ total mass $\div$ total volume: $108 \div 100 = 1.08$ g/cm³

True or false? When two liquids of different densities are mixed, the density of the mixture is the mean of the two densities.

False. You must work out the total mass and the total volume, then divide: density $=$ total mass $\div$ total volume.