Rates

Rates

A rate is a comparison between two quantities of different kinds, found by dividing one quantity by another.

For example:

If a man earns 1,000 shillings for working 2 hours, his rate of pay is:

1,000 ÷ 2 = 500 shillings per hour

This means he earns 500 shillings every hour he works.

Example 1

A man is paid 6,000/= for 8 hours of work.

(a) What is his rate of pay?

(b) At this rate, how much would he receive for 20 hours of work?

(c) At this rate, how long must he work to earn 30,000 shillings?

Solution:

(a) Rate of pay = 6,000 ÷ 8 = 750 shillings per hour

(b) For 20 hours:

20 × 750 = 15,000 shillings

(c) To earn 30,000:

30,000 ÷ 750 = 40 hours

Rates of Quantities of the Same Kind

Sometimes we compare quantities of the same type, such as height over time, to determine which is increasing faster.

Example 2

A student is growing plants and records their growth:

Plant A: 5 cm in 10 days

Plant B: 8 cm in 12 days

Which plant is growing more quickly?

Solution:

Growth rate of Plant A = 5 ÷ 10 = 0.5 cm per day

Growth rate of Plant B = 8 ÷ 12 ≈ 0.67 cm per day

Plant B is growing faster.

Currency Conversion Example

We can also use rates to convert between currencies.

Example 3

Suppose the exchange rate is 1 Euro = 650 Tsh.

(a) A tourist changes 200 Euros to Tanzanian shillings.

(b) A businesswoman wants to convert 2,080,000 Tsh to Euros.

Solution:

(a) 200 × 650 = 130,000 Tsh

(b) 2,080,000 ÷ 650 = 3,200 Euros