Grade 6 proportions word problems worksheet from K5 Learning.

Let's solve each of the proportions word problems step by step. These are all ratio and proportion problems, so we'll use equivalent ratios to find the unknown values.

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1. A car travels 120 miles in 3 hours (with a constant speed). How long will it take to travel 200 miles?

Step 1: Find the speed of the car.
$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{120 \text{ miles}}{3 \text{ hours}} = 40 \text{ miles per hour}
$$

Step 2: Use the speed to find time for 200 miles.
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{200}{40} = 5 \text{ hours}
$$

✔ Answer: 5 hours

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2. 50 apples cost $25. How much would 75 apples cost?

Step 1: Find the cost per apple.
$$
\text{Cost per apple} = \frac{25}{50} = \$0.50
$$

Step 2: Multiply by 75 apples.
$$
75 \times 0.50 = \$37.50
$$

✔ Answer: $37.50

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3. It takes Mike 18 minutes to finish reading 4 pages of a book. How long does it take for him to finish reading 30 pages?

Step 1: Find rate of reading (pages per minute).
$$
\text{Rate} = \frac{4 \text{ pages}}{18 \text{ minutes}} = \frac{2}{9} \text{ pages per minute}
$$

Step 2: Time for 30 pages:
$$
\text{Time} = \frac{30}{(2/9)} = 30 \times \frac{9}{2} = 135 \text{ minutes}
$$

Alternatively, set up a proportion:
$$
\frac{4}{18} = \frac{30}{x} \Rightarrow 4x = 540 \Rightarrow x = 135
$$

✔ Answer: 135 minutes

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4. Nathan packs 25 boxes in 2 hours. How many boxes can he pack in his 8-hour shift?

Step 1: Find packing rate.
$$
\frac{25 \text{ boxes}}{2 \text{ hours}} = 12.5 \text{ boxes per hour}
$$

Step 2: Multiply by 8 hours.
$$
12.5 \times 8 = 100 \text{ boxes}
$$

Or use proportion:
$$
\frac{25}{2} = \frac{x}{8} \Rightarrow 2x = 200 \Rightarrow x = 100
$$

✔ Answer: 100 boxes

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5. 13 candy bars weigh 26 ounces. What is the weight of 35 candy bars?

Step 1: Find weight per candy bar.
$$
\frac{26 \text{ oz}}{13} = 2 \text{ oz per candy bar}
$$

Step 2: Multiply by 35.
$$
35 \times 2 = 70 \text{ ounces}
$$

✔ Answer: 70 ounces

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6. A machine can produce 6 yards of fabric in 2 minutes. How much fabric can the machine produce in 1 hour?

Step 1: Convert 1 hour to minutes → 60 minutes.

Step 2: Find production rate.
$$
\frac{6 \text{ yards}}{2 \text{ minutes}} = 3 \text{ yards per minute}
$$

Step 3: Multiply by 60 minutes.
$$
3 \times 60 = 180 \text{ yards}
$$

Or use proportion:
$$
\frac{6}{2} = \frac{x}{60} \Rightarrow 2x = 360 \Rightarrow x = 180
$$

✔ Answer: 180 yards

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✔ Final Answers:

1. 5 hours
2. $37.50
3. 135 minutes
4. 100 boxes
5. 70 ounces
6. 180 yards

Let me know if you'd like these explained with diagrams or visual models!