GCSE Maths Practice: estimation

Question 7 of 10

Estimate speed by rounding both distance and time before using the formula.

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\( \begin{array}{l} \textbf{Estimate the speed:} \\ 298~\text{km in } 2.9~\text{hours} \end{array} \)

Choose one option:

Round both distance and time before dividing. State the rounded values clearly in your working.

Understanding Speed Estimation

Speed describes how fast something moves. It is calculated by dividing the distance travelled by the time taken. The standard formula is s = d ÷ t. In GCSE Maths, estimation questions test how well you can simplify numbers, reason logically, and communicate your process. Estimating speed is a practical skill used in everyday life — from planning journeys to checking if an answer seems reasonable.

Step-by-Step Method

  1. Round the distance: Choose an easy-to-handle value that is close to the given distance. For example, 298 km becomes 300 km.
  2. Round the time: Round 2.9 hours to 3 hours for simplicity.
  3. Apply the formula: Substitute your rounded values into s = d ÷ t.
  4. Compute mentally: 300 ÷ 3 = 100 km/h. This is your estimated speed.

Worked Examples

Example 1: A car travels 298 km in 2.9 hours.
Estimate speed → 300 ÷ 3 = 100 km/h.

Example 2: A cyclist covers 48 km in 1.2 hours.
Round → 50 ÷ 1 = 50 km/h.

Example 3: A train travels 850 km in 9.2 hours.
Round → 900 ÷ 9 = 100 km/h.

Common Mistakes

  • Forgetting to round both distance and time before dividing.
  • Using the wrong formula (time ÷ distance instead of distance ÷ time).
  • Mixing units, such as hours with minutes, without converting.
  • Not including the correct unit in the final answer (e.g., km/h or m/s).

Real-Life Applications

Speed estimation appears everywhere — drivers estimate average speed to plan travel time; athletes estimate running pace; pilots and sailors estimate speeds to stay on schedule. Engineers and scientists also use quick estimations to check whether sensor readings are realistic. For instance, if a vehicle tracking system shows 800 km/h for a car, an engineer instantly knows it must be an error because that’s beyond real-world limits.

FAQs

Q1: What units are best for speed estimation?
A: Use km/h or m/s depending on the context. For GCSE problems, km/h is common when distances are in kilometres and times in hours.

Q2: How accurate should my estimate be?
A: Estimates should show clear reasoning, not exact precision. Being within about 10% of the true value is usually acceptable.

Q3: Can estimation give a wrong sense of accuracy?
A: Only if rounding is careless. Always round sensibly — not too far from the original numbers.

Study Tip

In exams, always write the formula first, show your rounded values, and clearly display the estimated answer with correct units. This logical presentation earns method marks even if your final figure is slightly off. Practice estimating with different distances and times to strengthen mental calculation skills.

Summary

Estimation in speed problems strengthens your number sense and helps you judge whether results are realistic. By rounding distance and time appropriately, you can quickly reach an approximate speed that makes logical sense in real-world terms.