Let's solve each of the
proportions word problems step by step. These are all proportion-based problems, meaning we’ll use the idea that two ratios are equal.
---
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.
$$
\text{Speed} = \frac{120 \text{ miles}}{3 \text{ hours}} = 40 \text{ miles per hour}
$$
Step 2: Use the speed to find time for 200 miles.
$$
\text{Time} = \frac{200 \text{ miles}}{40 \text{ mph}} = 5 \text{ hours}
$$
✔ Answer: 5 hours
---
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.
$$
75 \times 0.50 = \$37.50
$$
Alternatively, set up a proportion:
$$
\frac{50}{25} = \frac{75}{x} \Rightarrow 50x = 1875 \Rightarrow x = 37.50
$$
✔ Answer: $37.50
---
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:
$$
\text{Time} = \frac{30}{(2/9)} = 30 \times \frac{9}{2} = 135 \text{ minutes}
$$
Or use proportion:
$$
\frac{4}{18} = \frac{30}{x} \Rightarrow 4x = 540 \Rightarrow x = 135
$$
✔ Answer: 135 minutes
---
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.
$$
12.5 \times 8 = 100 \text{ boxes}
$$
Proportion:
$$
\frac{25}{2} = \frac{x}{8} \Rightarrow 2x = 200 \Rightarrow x = 100
$$
✔ Answer: 100 boxes
---
5. 13 candy bars weigh 26 ounces. What is the weight of 35 candy bars?
Step 1: Weight per candy bar.
$$
\frac{26 \text{ oz}}{13} = 2 \text{ oz per candy bar}
$$
Step 2: Multiply by 35.
$$
35 \times 2 = 70 \text{ ounces}
$$
Proportion:
$$
\frac{13}{26} = \frac{35}{x} \Rightarrow 13x = 910 \Rightarrow x = 70
$$
✔ Answer: 70 ounces
---
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:
$$
1 \text{ hour} = 60 \text{ minutes}
$$
Step 2: Find production rate.
$$
\frac{6 \text{ yards}}{2 \text{ minutes}} = 3 \text{ yards per minute}
$$
Step 3: Multiply by 60 minutes.
$$
3 \times 60 = 180 \text{ yards}
$$
Proportion:
$$
\frac{6}{2} = \frac{x}{60} \Rightarrow 2x = 360 \Rightarrow x = 180
$$
✔ Answer: 180 yards
---
✔ Final Answers:
1.
5 hours
2.
$37.50
3.
135 minutes
4.
100 boxes
5.
70 ounces
6.
180 yards
These problems all rely on setting up proportions or calculating unit rates and then scaling them appropriately. Let me know if you'd like a visual explanation or practice problems!
Parent Tip: Review the logic above to help your child master the concept of ratio word problems worksheet 6th grade.
