Module 11: Average Speed

Phase 1: The X-Ray

Average speed is your Big Picture Journey. In the 11+, examiners love to show you two different speeds to tempt your child into a quick guess. The secret weapon is to ignore those middle speeds and zoom out. Success isn't about averaging numbers; it's about squashing the whole trip into one "Total Distance" and one "Total Time." If your child can collapse the journey into these two grand totals, the points are theirs.

The Road Trip "A car travels 15 miles in the morning and 25 miles in the afternoon. The trip took 2 hours. What was the average speed?"
The Morning Cycle "A cyclist travels 20km at 10km/h, then another 20km at 20km/h. What is the average speed for the whole trip?"
The Flight Path "A plane flies 600 miles at 300mph, then 400 miles at 200mph. Calculate the speed for the 1000-mile flight."

Phase 2: The Anatomy

Look at the Journey Line below. Point to the blue leg and the gold leg. We aren't interested in them as separate trips; we are watching them merge into one long road. Notice how the Meeting Point shifts. No matter where that point sits, the rule is the same: add the distances to get the "Road" and add the hours to get the "Time."

30 km 1.00 hrs
60 km 2.00 hrs
TOTAL: 90.00 km in 3.00 hours

Phase 3: The Engine

Adjust the sliders for each leg of the journey. Ask your child: "If we travel for longer, what happens to our average speed?" Watch the Trace Log—it shows you the logic of 'collapsing' the journey into one final calculation. Point out that the "Final Speed" only appears once we have both grand totals ready.

Phase 4: The Saboteur

The "Speed Splitter" Trap: If a car travels at 40mph then 60mph, bright children will often confidently shout "50mph!" It feels logical because 50 is right in the middle. This is a classic 11+ trap.

The Insider Fix: Tell your child: "Speeds don't matter until the very last step." You only find the average by dividing the Grand Totals. Unless the time spent at each speed is exactly the same (which it almost never is in exams), adding the speeds together will lead to a confident wrong answer.

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