FE Environmental Practice Question Solution included after investigation
CASE E-080 · FE

The Mixed Waste Batch That Was 5.67%, Not 4.5%

Averaging 8% and 1% gave 4.5%, but the two waste streams had different masses. The correct mixed concentration was 5.67% by mass.

▶ INTERACTIVE CASE FILE • 5–10 MIN • CLICK TO INVESTIGATE

Inspect, commit, prove, fix, and sign off.

Case E-080 engineering failure visual
HOW THIS WORKS

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Follow the investigation process used in the field — in five guided steps.

1

Inspect

Review the problem, diagram, and evidence.

2

Commit

Choose your hypothesis.

3

Prove

Run calculations and test your idea.

4

Fix

Select and validate a safe correction.

5

Sign Off

See the full debrief and key takeaways.

Case Brief

SAME PRINCIPLES. HIGHER STANDARDS.
PROBLEM STATEMENT

A waste-management process combines 100 kg of a waste containing 8 wt% of a target constituent with 50 kg of another waste containing 1 wt% of that constituent. Assume no reaction or mass loss during mixing. A note averages 8% and 1% and reports 4.5 wt%. Determine the correct mixed concentration.

Solid Hazardous Waste Environmental Design Verification Root Cause Analysis Safe Correction
E-080
INVESTIGATION WORKSPACE WORK THROUGH THE CASE — YOUR CHOICES MATTER.
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CASE CLOSED · ENGINEERING VERDICT

What actually failed — and what should change.

What failed

The two concentrations were averaged without weighting by stream mass.

What was missed

The 8 wt% stream had twice the mass of the 1 wt% stream.

Corrected model

Use a component mass balance to calculate the mixed mass fraction.

QUICK ANSWER

The first stream contains 8.0 kg constituent and the second contains 0.5 kg. Total constituent is 8.5 kg in 150 kg mixture, so the mixed concentration is 8.5/150×100=5.67 wt%.

ENGINEERING TAKEAWAY

Use a component mass balance: mixed mass fraction=(m1w1+m2w2)/(m1+m2).

CASE QUESTIONS

Questions this case should settle.

How do you calculate concentration after mixing two waste streams?

Use the mass-weighted average, wmix=(m1w1+m2w2)/(m1+m2), when there is no reaction or mass loss.

How much 1 wt% stream is needed to dilute 100 kg at 8 wt% to 5 wt%?

75 kg.

NEXT FE PRACTICE QUESTION

The Incinerator That Achieved 99.9%, Not 99%

Solid Hazardous Waste · 5–10 min

Continue Practice →
WHAT YOU’LL LEARN

Real failures. Lasting skills.

Each case is designed to build the judgment, analysis, and confidence you need for engineering exams — and beyond.

  • Apply core engineering concepts to real-world problems
  • Practice structured troubleshooting and analysis
  • Strengthen exam-ready thinking through realistic scenarios
COMMON QUESTIONS
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Are the cases aligned with engineering exams?

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What happens after I complete a case?

The sealed debrief unlocks with the root cause, corrected reasoning, fix, and takeaway.