Robot-themed math worksheet with 10 word problems covering topics like assembly lines, inventory, battery life, speed, weight, pricing, force, maintenance, precision, and revenue.

Let's solve each problem step by step and explain the reasoning behind each solution.

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1. Assembly Line: A robot assembly line produces 0.75 robots per minute. How many robots will the assembly line produce in 2 hours?

Step-by-step:
- 1 hour = 60 minutes → 2 hours = 120 minutes
- Production rate = 0.75 robots/minute
- Total robots = 0.75 × 120 = 90 robots

✔ Answer: 90 robots

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2. Inventory: A robot warehouse has 500 robots in stock. If 20% of the robots are defective, how many robots are not defective?

Step-by-step:
- 20% are defective → 80% are not defective
- 80% of 500 = (80/100) × 500 = 0.8 × 500 = 400 robots

✔ Answer: 400 robots are not defective

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3. Battery Life: A robot’s battery lasts for 3.5 hours on a full charge. If the robot was operating for 2.75 hours, how much battery life remains?

Step-by-step:
- Total battery life = 3.5 hours
- Used = 2.75 hours
- Remaining = 3.5 − 2.75 = 0.75 hours

✔ Answer: 0.75 hours (or 45 minutes) of battery life remains

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4. Robot Speed: Robot A can travel at a speed of 2.5 meters per second, while Robot B can travel at a speed of 3.75 meters per second. How much faster is Robot B than Robot A?

Step-by-step:
- Difference in speed = 3.75 − 2.5 = 1.25 meters per second

✔ Answer: Robot B is 1.25 m/s faster than Robot A

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5. Sensors: A robot has 8 sensors, each weighing 0.4 kilograms. What is the total weight of all the sensors?

Step-by-step:
- 8 sensors × 0.4 kg = 3.2 kilograms

✔ Answer: 3.2 kg

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6. Pricing: A company sells a robot for $850. If the company offers a discount of 15%, what is the discounted price of the robot?

Step-by-step:
- Discount amount = 15% of $850 = (15/100) × 850 = 0.15 × 850 = $127.50
- Discounted price = 850 − 127.50 = $722.50

✔ Answer: $722.50

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7. Durability: A robot can withstand a force of 7.8 newtons before breaking. If a load of 3.25 newtons is applied, how much more force can the robot handle before breaking?

Step-by-step:
- Maximum force = 7.8 N
- Applied force = 3.25 N
- Remaining capacity = 7.8 − 3.25 = 4.55 newtons

✔ Answer: 4.55 newtons

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8. Maintenance: A robot requires maintenance every 500 operating hours. If a robot has been operating for 3,750 hours, how many maintenance sessions has it undergone?

Step-by-step:
- Number of sessions = Total hours ÷ Interval = 3,750 ÷ 500 = 7.5

But since maintenance is done *every* 500 hours, we count full intervals:
- After 500, 1000, 1500, ..., up to 3750
- This is an arithmetic sequence: 500 × 7 = 3500 (7th session)
- 3750 > 3500 → So it has completed 7 full sessions and is halfway through the 8th.
- But the question asks "how many maintenance sessions has it undergone?" — meaning completed ones.

✔ Answer: 7 maintenance sessions

> Note: Some might interpret “has undergone” as including partial, but typically it means completed sessions. So 7.

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9. Precision: A robot arm can position an object with an accuracy of 0.01 millimeters. If the robot needs to position an object 0.07 millimeters accurately, how many times does it need to adjust?

Step-by-step:
- Accuracy per adjustment = 0.01 mm
- Required precision = 0.07 mm
- Number of adjustments needed = 0.07 ÷ 0.01 = 7

✔ Answer: 7 adjustments

> Interpretation: Each adjustment improves position by 0.01 mm, so to reach 0.07 mm accuracy, it must make 7 such adjustments.

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10. Revenue: A company sold 15 robots at a price of $3,500 each. If the company’s revenue is subject to an 8.5% sales tax, what is the total amount of tax paid?

Step-by-step:
- Total revenue = 15 × 3,500 = $52,500
- Sales tax = 8.5% of $52,500 = (8.5/100) × 52,500 = 0.085 × 52,500 = $4,462.50

✔ Answer: $4,462.50

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✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 90 robots |
| 2 | 400 robots |
| 3 | 0.75 hours |
| 4 | 1.25 m/s |
| 5 | 3.2 kg |
| 6 | $722.50 |
| 7 | 4.55 newtons |
| 8 | 7 sessions |
| 9 | 7 times |
| 10 | $4,462.50 |

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