A construction engineering problem uses Crew productivity. Given production rate (P) = 7.0000 units/hr; duration (t) = 158.0 hr, determine the total quantity (Q) in units.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = P \times t$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: production rate (P) = 7.0000 units/hr, duration (t) = 158.0 hr$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Q = 1106\ \text{units}$$

6. Step 6 — Check: returning Q = 1,106 units to

   $$Q = P \times t$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,212 — kept a factor of two that cancels in the correct rearrangement.
• 553.0 — dropped that same factor in the other direction.
• 1,217 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 361.0 $/unit; quantity (Q) = 7,601 units, determine the total cost (C) in $.

Start with the thinking

• The governing relation printed in this handbook section is Total cost from unit cost.
• Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = c_u \times Q$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: unit cost (cu) = 361.0 $/unit, quantity (Q) = 7,601 units.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 2743961\ \text{\$}$$

6. Step 6 — Check: returning C = 2,743,961 $ to

   $$C = c_u \times Q$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 5,487,922 — kept a factor of two that cancels in the correct rearrangement.
• 1,371,981 — dropped that same factor in the other direction.
• 3,018,357 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Crew productivity. Given duration (t) = 84.0000 hr; total quantity (Q) = 2,936 units, determine the production rate (P) in units/hr.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• Everything except P is given, so isolate P symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = P \times t$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3

   $$List the givens: duration (t) = 84.0000 hr, total quantity (Q) = 2,936 units$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 34.9524\ \text{units/hr}$$

6. Step 6 — Check: returning P = 34.9524 units/hr to

   $$Q = P \times t$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 69.9048 — kept a factor of two that cancels in the correct rearrangement.
• 17.4762 — dropped that same factor in the other direction.
• 38.4476 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Total cost from unit cost. Given quantity (Q) = 840.0 units; total cost (C) = 334,007 $, determine the unit cost (cu) in $/unit.

Start with the thinking

• The governing relation printed in this handbook section is Total cost from unit cost.
• Everything except cu is given, so isolate cu symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = c_u \times Q$$

2. Step 2 — Rearrange the relation so that cu stands alone on the left-hand side.

3. Step 3 — List the givens: quantity (Q) = 840.0 units, total cost (C) = 334,007 $.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$cu = 397.6\ \text{\$/unit}$$

6. Step 6 — Check: returning cu = 397.6 $/unit to

   $$C = c_u \times Q$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 795.3 — kept a factor of two that cancels in the correct rearrangement.
• 198.8 — dropped that same factor in the other direction.
• 437.4 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Crew productivity. Given production rate (P) = 85.0000 units/hr; total quantity (Q) = 1,251 units, determine the duration (t) in hr.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• Everything except t is given, so isolate t symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = P \times t$$

2. Step 2 — Rearrange the relation so that t stands alone on the left-hand side.

3. Step 3 — List the givens: production rate (P) = 85.0000 units/hr, total quantity (Q) = 1,251 units.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$t = 14.7176\ \text{hr}$$

6. Step 6 — Check: returning t = 14.7176 hr to

   $$Q = P \times t$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 29.4353 — kept a factor of two that cancels in the correct rearrangement.
• 7.3588 — dropped that same factor in the other direction.
• 16.1894 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 103.5 $/unit; total cost (C) = 324,332 $, determine the quantity (Q) in units.

Start with the thinking

• The governing relation printed in this handbook section is Total cost from unit cost.
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = c_u \times Q$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3 — List the givens: unit cost (cu) = 103.5 $/unit, total cost (C) = 324,332 $.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Q = 3134\ \text{units}$$

6. Step 6 — Check: returning Q = 3,134 units to

   $$C = c_u \times Q$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 6,267 — kept a factor of two that cancels in the correct rearrangement.
• 1,567 — dropped that same factor in the other direction.
• 3,447 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Crew productivity. Given production rate (P) = 91.0000 units/hr; duration (t) = 150.0 hr, determine the total quantity (Q) in units.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• Everything except Q is given, so isolate Q symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = P \times t$$

2. Step 2 — Rearrange the relation so that Q stands alone on the left-hand side.

3. Step 3

   $$List the givens: production rate (P) = 91.0000 units/hr, duration (t) = 150.0 hr$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$Q = 13650\ \text{units}$$

6. Step 6 — Check: returning Q = 13,650 units to

   $$Q = P \times t$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 27,300 — kept a factor of two that cancels in the correct rearrangement.
• 6,825 — dropped that same factor in the other direction.
• 15,015 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Total cost from unit cost. Given unit cost (cu) = 441.5 $/unit; quantity (Q) = 8,747 units, determine the total cost (C) in $.

Start with the thinking

• The governing relation printed in this handbook section is Total cost from unit cost.
• Everything except C is given, so isolate C symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = c_u \times Q$$

2. Step 2 — Rearrange the relation so that C stands alone on the left-hand side.

3. Step 3 — List the givens: unit cost (cu) = 441.5 $/unit, quantity (Q) = 8,747 units.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$C = 3861801\ \text{\$}$$

6. Step 6 — Check: returning C = 3,861,801 $ to

   $$C = c_u \times Q$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 7,723,601 — kept a factor of two that cancels in the correct rearrangement.
• 1,930,900 — dropped that same factor in the other direction.
• 4,247,981 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Crew productivity. Given duration (t) = 19.0000 hr; total quantity (Q) = 4,744 units, determine the production rate (P) in units/hr.

Start with the thinking

• The governing relation printed in this handbook section is Crew productivity.
• Everything except P is given, so isolate P symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$Q = P \times t$$

2. Step 2 — Rearrange the relation so that P stands alone on the left-hand side.

3. Step 3

   $$List the givens: duration (t) = 19.0000 hr, total quantity (Q) = 4,744 units$$

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$P = 249.7\ \text{units/hr}$$

6. Step 6 — Check: returning P = 249.7 units/hr to

   $$Q = P \times t$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 499.4 — kept a factor of two that cancels in the correct rearrangement.
• 124.8 — dropped that same factor in the other direction.
• 274.7 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis

A construction engineering problem uses Total cost from unit cost. Given quantity (Q) = 9,864 units; total cost (C) = 425,980 $, determine the unit cost (cu) in $/unit.

Start with the thinking

• The governing relation printed in this handbook section is Total cost from unit cost.
• Everything except cu is given, so isolate cu symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Construction Engineering items reward recognising the unknown before touching a calculator.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$C = c_u \times Q$$

2. Step 2 — Rearrange the relation so that cu stands alone on the left-hand side.

3. Step 3 — List the givens: quantity (Q) = 9,864 units, total cost (C) = 425,980 $.

4. Step 4 — Substitute the given values into the rearranged relation.

5. Step 5 — Evaluate:

   $$cu = 43.1853\ \text{\$/unit}$$

6. Step 6 — Check: returning cu = 43.1853 $/unit to

   $$C = c_u \times Q$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 86.3706 — kept a factor of two that cancels in the correct rearrangement.
• 21.5927 — dropped that same factor in the other direction.
• 47.5039 — rounded an intermediate value before the final step.

Reference: FE Reference Handbook — Construction Engineering → Earned-Value Analysis