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5.1 Rates, Distance & Averages

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ADF YOU Session Job Opportunities Assessment

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1 Introduction & JOA Overview

1.1 What the JOA Is and Why the ADF Uses It 1.2 Current Exam Facts (51 Questions, 20 Minutes) 1.3 JOA vs YOU Session vs the Wider Process

2 Logistics, Access & Attempt Rules

2.1 Access, Devices & Browser Setup 2.2 Three Attempts & Six-Month Wait 2.3 After the JOA: JOR and Recruiter Contact

3 Official Tips & Test-Day Strategy

3.1 Official Top Tips & Natural Ability 3.2 Pacing, Flagging & Order of Attack 3.3 Integrity, Help Rules & Supervised Verification

4 Numerical Reasoning: Series & Matrices

4.1 Number Series Patterns 4.2 Number Matrices & Missing Values 4.3 Numerical Speed & Estimation Under Time

5 Numerical Reasoning: Word Problems

5.1 Rates, Distance & Averages 5.2 Ratios, Proportions & Percentage Reasoning 5.3 Multi-Step Numerical Reasoning

6 Verbal Reasoning

6.1 Word Meaning & Relationships 6.2 Verbal Analogies 6.3 Verbal Odd-One-Out 6.4 Verbal Logic & Multi-Statement Proofs

7 Abstract Reasoning: Sequences & Rules

7.1 Sequence & Next-Item Patterns 7.2 Rotation, Reflection & Orientation 7.3 Multi-Attribute Pattern Rules

8 Abstract Reasoning: Odd-One-Out & Complex Figures

8.1 Shape Odd-One-Out 8.2 Complex Figures & Spatial-Style Abstract Items 8.3 Abstract Speed Habits

9 Integrated Prep & Common Traps

9.1 Mixed Timed Practice 9.2 Common Traps Across All Item Types 9.3 Day-of Checklist

10 Results & Next Steps

10.1 Understanding the Job Opportunities Report 10.2 Pathway After the JOA

5.1 Rates, Distance & Averages

Key Takeaways Explain This Topic AI

JOA numerical word problems test timed reasoning with quantities — often rate, distance, and time — not a school Mathematical Ability paper.

Core relation: time = distance ÷ speed (and rearrangements distance = speed × time, speed = distance ÷ time); keep units consistent before you divide.

Average rate is rarely the arithmetic mean of two speeds when times differ; use total distance ÷ total time.

Official-style items may use typed numeric answers (for example, hours for a cycle ride); enter the exact value the stem asks for.

Under ~23.5 seconds average per JOA item, set up the relation quickly, compute cleanly, and flag multi-unit messes for a return pass.

Last updated: August 2026

Word Problems on the JOA — Reasoning, Not a Maths Curriculum

On the Job Opportunities Assessment (ADF-RECREF132, revised 27 June 2025), numerical items sit inside one mixed 51-question / 20-minute assessment with verbal and abstract reasoning. The official guide’s numerical examples include word-problem styles such as rate and distance — for instance, a cyclist covering a stated distance at a stated speed, with a typed answer for how many hours the trip takes. That design samples how you extract quantities and apply a simple relation under time , not whether you can sit a separate school Mathematical Ability paper.

This chapter deliberately avoids algebra curricula, geometry proofs, trigonometry, Pythagoras, and SOH-CAH-TOA as JOA “domains.” Those belong to older two-test formats that are retired . What you need for modern JOA word problems is fluent quantity reasoning : read the stem, identify what is asked, map the numbers onto a small relation, compute carefully, and move on.

Why rate problems appear so often

Rate problems are ideal for a natural-ability test because they require:

Reading discipline — which number is distance, which is speed, which is time?

Relation selection — which form of the rate equation fits the unknown?

Unit attention — hours vs minutes, km vs m, per hour vs per minute.

Clean arithmetic under a ~ 23.5-second average budget (1,200 seconds ÷ 51).

None of that requires advanced school theory. All of it rewards calm process.

The Core Rate Family: Distance, Speed, Time

The single relation that powers most JOA-style rate items is: distance = speed × time \text{distance} = \text{speed} \times \text{time} distance = speed × time

Rearranged for the two common unknowns:

  • Unknown Formula When you use it
  • Time time = distance ÷ speed “How long did the trip take?”
  • Speed speed = distance ÷ time “What was the average speed?”
  • Distance distance = speed × time “How far did they travel?”
  • Official-style worked example (typed hours)

Stem (paraphrased style): Abby cycled 70 km at 20 km/h . How many hours did the ride take?

Setup: Unknown is time. Units already match (km and km/h). time = 70 20 = 3.5 hours \text{time} = \frac{70}{20} = 3.5 \text{ hours} time = 20 70 ​ = 3.5 hours

If the interface wants a typed number, enter 3.5 (or the exact format the on-screen instruction allows). Do not invent a multiple-choice option that is not there. Do not convert to minutes unless the stem asks for minutes (3.5 hours = 210 minutes — a classic distractor if you misread the unit of the answer).

Worked example: find speed

A patrol covers 45 km in 1.5 hours at constant speed. What is the speed in km/h? speed = 45 1.5 = 30 km/h \text{speed} = \frac{45}{1.5} = 30 \text{ km/h} speed = 1.5 45 ​ = 30 km/h

Quick check: 30 × 1.5 = 45 — closes the loop.

Worked example: find distance

A vehicle travels at 80 km/h for 2.25 hours . How far does it go? distance = 80 × 2.25 = 180 km \text{distance} = 80 \times 2.25 = 180 \text{ km} distance = 80 × 2.25 = 180 km

Tip under time: 2.25 = 2 + 1/4, so 80 × 2 = 160 and 80 × 0.25 = 20; total 180. Decomposition beats long multiplication when the clock is running.

  • Unit consistency before any division
  • Most rate errors are unit errors, not “bad maths.”
  • Stem mix Fix before computing
  • Distance in km, speed in m/h Convert one side (1 km = 1,000 m)
  • Time in minutes, speed in per hour Convert minutes to hours (÷ 60) or speed to per minute
  • Answer asked in minutes Compute hours, then × 60 — or work entirely in minutes
  • “Per day” vs “per hour” rates Align the time base of every rate in the stem

Micro-example: 90 km at 30 km/h takes 3 hours. If the stem asked for minutes , the answer is 180 — not 3. Always re-read the unit of the unknown in the last line of the stem.

Average Rate Traps (Not the Mean of Speeds)

Candidates often average two speeds with ( v 1 + v 2 ) / 2 (v_1 + v_2) / 2 ( v 1 ​ + v 2 ​ ) /2 . That is correct only in special cases (for example, equal time at each speed). When a journey has legs with different speeds and different times, or equal distances at different speeds, the honest average speed is: average speed = total distance total time \text{average speed} = \frac{\text{total distance}}{\text{total time}} average speed = total time total distance ​

Worked trap: equal distances, different speeds

A runner covers 10 km at 10 km/h , then another 10 km at 20 km/h . What is the average speed for the full 20 km?

Wrong instinct: ((10 + 20) / 2 = 15) km/h.

Correct process:

  • Time leg 1: (10 / 10 = 1) hour
  • Time leg 2: (10 / 20 = 0.5) hour
  • Total distance = 20 km; total time = 1.5 hours
  • Average speed = (20 / 1.5 ≈ 13.33) km/h

The average is below the midpoint of 10 and 20 because more time was spent on the slower leg. JOA-style options may include 15 as a deliberate distractor for candidates who average speeds.

Worked case: equal times

If someone drives 1 hour at 60 km/h and 1 hour at 100 km/h:

  • Total distance = 60 + 100 = 160 km
  • Total time = 2 hours
  • Average speed = 80 km/h

Here the arithmetic mean of speeds matches because times are equal — but you still arrived via total distance ÷ total time, which is the safe habit for every stem.

Partial-rate and “how much longer” stems

Some items give a rate and a completed fraction of work or distance, then ask for remaining time.

Example: A tank fills at 200 litres per hour. After 1.5 hours it holds 300 litres and is still filling at the same rate toward a 500-litre capacity. How many more hours to full?

  • Remaining volume = 500 − 300 = 200 litres
  • Remaining time = 200 ÷ 200 = 1 hour

Alternatively: full time would be 500 ÷ 200 = 2.5 hours; already used 1.5; remaining 1 hour. Same answer, two setups — pick the one that clicks faster.

JOA pacing for rate items

  • Situation Action
  • Clean numbers, units match Solve immediately (often 15–25 seconds)
  • Answer unit differs from working unit Pause one second to convert; do not submit the pre-conversion value
  • Average-rate stem with two speeds Force total distance ÷ total time; ignore the midpoint temptation
  • Messy unit chain (km, minutes, m/s) Flag and return after banking easier items
  • Typed numeric entry Type carefully; match decimals/integers the stem implies

Remember the official goal: complete as many as possible , as fast and accurately as possible — finishing all 51 is rare. A rate item you can close in 20 seconds is high value; a unit jungle that eats 70 seconds is a flag candidate.

Process checklist (use until automatic)

Underline the unknown and its unit (hours? km/h? minutes?).

List given quantities with units.

Pick the formula form (time / speed / distance).

Align units before arithmetic.

Compute , then sense-check (is 3.5 hours plausible for 70 km at 20 km/h? Yes.).

Submit or type the value in the requested unit; move on.

Practice this checklist on short mixed drills so that under JOA pressure the steps collapse into one smooth pass — natural ability displayed cleanly, not school-exam theatrics.