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UAT-UK SPEC: M3MODULE: MATHEMATICS 1TOPIC ID: ARCH-M1-05

Two-Component Mixing, Dilution Alligation & Combined Work Rates

Master Two-Component Mixing, Dilution Alligation & Combined Work Rates on the ESAT Mathematics 1 paper. Traditional classroom derivations waste valuable seconds. Using the 2-step Sub-90 invariant elimination method compresses solve time to 45s, saving +105s per question.

Standard Classroom Time
150s
Textbook multi-line derivations bleed exam clock
Sub-90 Target Pace
45s
Comfortably below the 88.8s per-question limit
Time Saved for Review
+105s
Banks clock buffer across 27 questions

2-Step Sub-90 Shortcut Formula

How to eliminate intermediate algebra and solve under 45 seconds.

Launch Interactive Lesson
STEP 1 • SETUP INVARIANT (LINE 1)10–15s
Line 1 (Fraction Product): PR=PQ×QR=53×67\frac{P}{R} = \frac{P}{Q} \times \frac{Q}{R} = \frac{5}{3} \times \frac{6}{7}.

Establish the structural invariant and eliminate impossible options immediately.

STEP 2 • FAST SOLVE (LINE 2)15–25s
Line 2 (Cancel 33): 107  ⟹  10:7\frac{10}{7} \implies 10 : 7 (20s).

Evaluate the simplified expression using integer factoring or unit elimination.

Distractor Trap Forensics

The predictable cognitive traps engineered by examiners into the wrong options.

TRAP #1subsystem_isolation_trap

Dividing solute mass by added water volume V(added) instead of final total volume V(initial) + V(added)

Forgetting that adding solute or solvent changes the total denominator of the mixture.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #2intermediate_stop_trap

Adding times T₁ + T₂ instead of rates 1/T₁ + 1/T₂

Combining work times additively rather than inverting the sum of individual rates.

Sub-90 Fix: Test invariants before expanding equations.
TRAP #3factor_of_two_or_stoichiometry_trap

Chain ratio Q:R = a:b and R:S = c:d combined as a*d : b*c instead of a*c : b*d

Cross-multiplying the wrong terms when bridging the shared middle variable R.

Sub-90 Fix: Test invariants before expanding equations.

Try 1 Timed Question: Two-Component Mixing, Dilution Alligation & Combined Work Rates

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Full Lesson All 15 Questions (ARCH-M1-05)
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ARCH-M1-05: Two-Component Mixing, Dilution Alligation & Combined Work Rates (Sample)Mathematics 1
00:00.0
SUB-90 ZONE (<45S)
0.0s45s Sub-9090s ESAT Budget150s Classroom
Question 1 of 1ARCH-M1-05 (6-Card Lesson)Format: Standard 5-Option
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Question 1 of 1 • 90s Target

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