Let's solve each of the
proportions word problems step by step. These are all proportion problems, meaning we can use
ratios to find unknown values.
---
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.
$$
75 \times 0.50 = \$37.50
$$
✔ 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 time per page.
$$
\text{Time per page} = \frac{18}{4} = 4.5 \text{ minutes per page}
$$
Step 2: Multiply by 30 pages.
$$
30 \times 4.5 = 135 \text{ minutes}
$$
✔ 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 rate of packing.
$$
\text{Boxes per hour} = \frac{25}{2} = 12.5 \text{ boxes/hour}
$$
Step 2: Multiply by 8 hours.
$$
12.5 \times 8 = 100 \text{ boxes}
$$
✔ Answer: 100 boxes
---
5. 13 candy bars weigh 26 ounces. What is the weight of 35 candy bars?
Step 1: Find weight per candy bar.
$$
\frac{26}{13} = 2 \text{ ounces per candy bar}
$$
Step 2: Multiply by 35.
$$
35 \times 2 = 70 \text{ ounces}
$$
✔ 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 per minute.
$$
\frac{6 \text{ yards}}{2 \text{ minutes}} = 3 \text{ yards per minute}
$$
Step 3: Multiply by 60 minutes.
$$
3 \times 60 = 180 \text{ yards}
$$
✔ 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 involve setting up proportions or using unit rates to scale quantities. The key idea is:
if the rate is constant, you can multiply or divide proportionally.
Parent Tip: Review the logic above to help your child master the concept of direct proportion worksheet.
