Unit Rates worksheet with word problems and mathematical exercises for students.

I'll solve each unit rate problem step by step.

Problem 1: If a person runs five miles in 45 minutes, how long will it take them to run eight miles at the same rate?

First, I need to find the rate (time per mile):
- 45 minutes ÷ 5 miles = 9 minutes per mile

Now multiply by 8 miles:
- 9 minutes/mile × 8 miles = 72 minutes

Problem 2: Rosa needs to buy 20 donuts for a class party. A package of six donuts cost $2.50. A package of 15 donuts costs $6.25. How much will the donuts cost if Rosa buys them by choosing the better buy?

Let me calculate the unit price for each option:
- Package of 6: $2.50 ÷ 6 donuts = $0.4167 per donut (approximately)
- Package of 15: $6.25 15 donuts = $0.4167 per donut (approximately)

They're actually the same unit price! Let me verify:
- 6 donuts: $2.50/6 = $0.4166... per donut
- 15 donuts: $6.25/15 = $0.4166... per donut

Since they have the same unit price, I should choose the combination that gives exactly 20 donuts with the least waste.

Option A: Buy packages of 6
- Need 20 donuts
- 3 packages of 6 = 18 donuts (need 2 more)
- 4 packages of 6 = 24 donuts (4 extra)
- Cost: 4 × $2.50 = $10.00

Option B: Buy packages of 15
- Need 20 donuts
- 1 package of 15 = 15 donuts (need 5 more)
- 2 packages of 15 = 30 donuts (10 extra)
- Cost: 2 × $6.25 = $12.50

Option C: Mix both
- 1 package of 15 + 1 package of 6 = 21 donuts (1 extra)
- Cost: $6.25 + $2.50 = $8.75

The best deal is Option C: $8.75

Problem 3: Dave has to fill up a 200-gallon water tank. There are already 50 gallons of water in it, and the pump Dave uses can fill 25 gallons per hour. How many hours will it take for him to fill the tank?

First, find how many gallons are needed:
- 200 - 50 = 150 gallons needed

Now divide by the rate:
- 150 gallons ÷ 25 gallons/hour = 6 hours

Problem 4: The Chen family travels 50 miles in five hours. What is their average rate of speed in miles per hour?

Rate = Distance ÷ Time
- 50 miles ÷ 5 hours = 10 miles per hour

Problem 5: A used car lot pays an employee on extra $500 on top of what they sell eight cars in a quarter. What rate is the company paying per car, for the bonus?

Wait, let me re-read this. It says "pays an employee on extra $500" - this seems unclear. Let me interpret it as: the employee gets an extra $500 bonus when they sell 8 cars in a quarter.

Rate per car = $500 ÷ 8 cars = $62.50 per car

Problem 6: Convert 37 yards to feet using the correct ratio. Show your work.

I know that 1 yard = 3 feet

So: 37 yards × 3 feet/yard = 111 feet

Final Answer:
1. 72 minutes
2. $8.75
3. 6 hours
4. 10 miles per hour
5. $62.50 per car
6. 111 feet