Rate — O/L Mathematics

What must I remember about Rate?

• A rate expresses the relationship between two quantities measured in different units: Rate = (First Quantity) / (Second Quantity).
• Speed is the rate of change of distance with respect to time: Speed = Distance / Time; Distance = Speed × Time; Time = Distance / Speed.
• Uniform speed means equal distances are covered in equal intervals of time; Average Speed = Total Distance / Total Time.
• Unit conversion of speed: Multiply km/h by (5 / 18) to convert to m/s; multiply m/s by (18 / 5) to convert to km/h.
• Volumetric flow rate: Rate of discharge = Volume of liquid / Time taken (units: litres/minute, m³/second).

Test yourself (1 minute)

1. The average speed trap

   Average speed is NEVER the simple arithmetic mean of two speeds; it must always be calculated as (Total Distance) / (Total Time).

2. Unit compatibility

   If speed is in km/h and time is in minutes, convert time to hours (e.g., 45 minutes = 45/60 = 0.75 hours) before multiplying.

3. Tank filling/emptying problems

   If pipe A fills a tank in 3 hours (rate = 1/3 tank/h) and pipe B empties in 4 hours (rate = 1/4 tank/h), net filling rate = 1/3 - 1/4 = 1/12 tank/h.

Practise Rate questions today

Source: NIE G.C.E. (O/L) Mathematics Syllabus (Grade 10, Unit 21)

What comes next?

Next in the syllabus

Where does Rate fit in the syllabus?

Grade 10 · Term 3