P5 Speed-Distance-Time Problems: The Systematic Approach That Stops Careless Errors

Of all the topics I taught in P5, speed-distance-time problems generated more stress, more crossed-out working, and more tearful homework sessions than almost anything else. Not because the maths is hard — the core calculations are multiplication and division — but because the structure of these problems trips students up before they even pick up their pencil.

Let me show you the approach I taught my Kowloon City P5 students. Once they had this system, their error rate on speed problems dropped dramatically. The same method works at home tonight.

Why Speed Problems Go Wrong

The root cause of most errors isn't calculation mistakes. It's one of three things:

1. Unit confusion Speed might be in km/h, but the time given is in minutes. Students plug numbers into formulas without checking whether the units match. The answer looks plausible but is off by a factor of 60.

2. Triangle formula misremembering Students are taught the "DST triangle" (Distance = Speed × Time, drawn as a triangle with D on top). When stressed in an exam, they misremember which operations to use for each variable.

3. Multi-step blindness Harder P5 problems require calculating a middle quantity (e.g., total distance) before finding the final answer. Students jump to the end goal and don't know what intermediate step is missing.

The Three-Step System

Here is the exact system I taught. It takes about 90 seconds to apply before calculating anything, and it prevents nearly all of the errors above.

Step 1: Extract and label Read the entire problem. Write down the three values in a box:

• D = ___
• S = ___
• T = ___

Fill in what you know. Leave blanks for what you need to find. This forces you to read carefully and notice unit inconsistencies.

Step 2: Convert units before anything else If Speed is in km/h and Time is in minutes: convert minutes to hours first. 30 minutes = 30/60 = 0.5 hours 45 minutes = 45/60 = 0.75 hours

Never put unconverted values into a formula.

Step 3: Apply the formula you've confirmed Only now pick up the pencil and calculate. With values checked and units matched, the arithmetic is straightforward.

Worked Example: The Classic Two-Part Problem

"A car travels 120 km at 60 km/h, then 90 km at 45 km/h. What is the average speed for the whole journey?"

This is a common P5 exam question. Here's how a student without a system approaches it: they add 60 and 45, divide by 2, write 52.5 km/h. Wrong.

Here's how a student with the system approaches it:

Journey 1: D = 120 km, S = 60 km/h, T = ? T = D ÷ S = 120 ÷ 60 = 2 hours

Journey 2: D = 90 km, S = 45 km/h, T = ? T = D ÷ S = 90 ÷ 45 = 2 hours

Total: Total D = 120 + 90 = 210 km Total T = 2 + 2 = 4 hours Average Speed = 210 ÷ 4 = 52.5 km/h

Wait — the answer is the same? Yes, in this specific case. But notice what changed: the process is correct. If the second leg had been 90 km at 30 km/h, the naive approach (averaging the speeds) would have given 45 km/h, while the correct answer is 48 km/h. Averaging speeds only works when the times are equal, not when the distances are equal. The system catches this.

Unit Conversion Quick Reference

Post this on your child's desk during homework:

Given Time	Convert To Hours By
30 minutes	÷ 2 (= 0.5 h)
45 minutes	÷ 60 × 45 (= 0.75 h)
1 h 30 min	= 1.5 h
1 h 15 min	= 1.25 h
20 minutes	÷ 3 (= 0.333... h)

The last one — 20 minutes — appears in TSA-style questions deliberately, because students who haven't practised non-round conversions get decimal errors. If your child struggles with these, practice them separately before attempting full speed problems.

The "Is This Reasonable?" Check

After every speed problem, ask your child: "Does this answer make sense?"

If a cyclist's speed comes out as 200 km/h, something went wrong. If a walk across Hong Kong takes 3 minutes, check the units. The reasonableness check catches unit errors that the calculation didn't.

Specifically, I'd tell my students: a fast runner does about 15 km/h. A car on a highway does about 100 km/h. A bicycle does about 20 km/h. If your answer is wildly outside these ranges, re-examine your working.

Practice Strategy

Speed problems reward systematic practice more than cramming. I recommend:

• 5 problems per week, not 20 the night before an exam
• Always use the extract-and-label step, even for easy problems — you're building habit, not just getting answers
• Mix question types: one-step, two-step, and average speed problems all appear in HK primary exams

The students who become genuinely good at speed problems are the ones who never skip the setup. It feels slow at first. After two weeks, it becomes automatic — and then it actually speeds them up, because they're not backtracking to fix unit errors.

Start tonight with the three-step system. The first time your child automatically writes "D = , S = , T =" before calculating, you'll know it's working.