Rates

A rate is a measure of quantity, and comparing one quantity with another of different kind.

Example 1

If a car takes two hours to travel a distance of 160 km. then we will say that it is travelling at an average rate of 80 km per hour.

If two kilograms of maize meal is sold for sh. 38.00, then we say that maize meal is selling at the rate of sh. 19.00 per kilogram.

Example 2

What is the rate of consumption per day if twelve bags of beans are consumed in 1 20 days?

To find the rate of consumption per day, we divide the total consumption by the number of days.

Given:

- Total consumption of beans = 12 bags

- Number of days = 120 days

Rate of consumption per day = Total consumption / Number of days

Rate of consumption per day = 12 bags / 120 days

To simplify this, we divide both the numerator and denominator by their greatest common divisor, which is 12.

Rate of consumption per day = (12 bags ÷ 12) / (120 days ÷ 12)

Rate of consumption per day = 1 bag / 10 days

So, the rate of consumption per day is 1 bag of beans consumed every 10 days.

Example 3

A laborer’s wage is sh.240 per eight hours working day. What is the rate of payment per hour?

To find the rate of payment per hour, we divide the total wage by the number of hours worked.

Given:

- Total wage for a working day = sh. 240

- Number of hours worked in a day = 8 hours

Rate of payment per hour = Total wage / Number of hours

Rate of payment per hour = sh. 240 / 8 hours

To find the rate of payment per hour, we simply divide the total wage by the number of hours worked:

Rate of payment per hour = sh. 240 / 8 hours

Calculating:

Rate of payment per hour = sh. 30 per hour

So, the rate of payment per hour is sh. 30.

Unit Rate

A unit rate is a rate with a denominator of 1.

A common example of a unit rate is driving speed. For example, 20 mph, read as ”20 miles per hour” can be written as follows.

Example 4:

A trucker drove 100 miles in 2 hours. Find the unit rate.

To find the unit rate, we divide the total distance traveled by the time taken.

Given:
- Total distance traveled = 100 miles
- Time taken = 2 hours

Unit rate = Total distance / Time taken

Unit rate = 100 miles / 2 hours

Unit rate = 50 miles per hour

So, the unit rate is 50 miles per hour. This means that the trucker drove at an average speed of 50 miles per hour.