Rate Word Problems - Teach-nology - Free Printable

Of course! Let's solve each of the rate word problems step by step.

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Problem 1:

> Nathan paid $56.25 for 75 cans of juice. If he were to buy 3 cans at the same price, how much would he have to pay?

Solution:

First, find the unit rate — the cost per can.

> Cost per can = Total cost ÷ Number of cans
> = $56.25 ÷ 75
> = $0.75 per can

Now, multiply by 3 cans:

> Cost for 3 cans = 3 × $0.75 = $2.25

✔ Answer: $2.25

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Problem 2:

> A bread recipe calls for 4 eggs for every 1½ pounds of flour. If you had 12 pounds of flour, how many eggs would you need to make all the bread that you could?

Solution:

This is a proportion problem.

We know:
- 4 eggs → 1.5 pounds of flour

We want to find how many eggs (let’s call it *x*) are needed for 12 pounds of flour.

Set up the proportion:

> 4 eggs / 1.5 lbs = x eggs / 12 lbs

Cross-multiply:

> 1.5 × x = 4 × 12
> 1.5x = 48
> x = 48 ÷ 1.5
> x = 32

✔ Answer: 32 eggs

*(Note: You can also think of it as “how many 1.5-pound portions are in 12 pounds?” → 12 ÷ 1.5 = 8. Then 8 × 4 eggs = 32 eggs.)*

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Problem 3:

> Jenny peddled her bike 11 miles in 45 minutes. If she travelled at the same speed, how far would she travel in 2 hours?

Solution:

First, convert 2 hours into minutes to match units:

> 2 hours = 120 minutes

Find her rate in miles per minute:

> Rate = Distance ÷ Time = 11 miles ÷ 45 minutes ≈ 0.2444... miles/minute

Now multiply by 120 minutes:

> Distance = 0.2444... × 120 = (11/45) × 120

Let’s simplify:

> (11 × 120) ÷ 45 = 1320 ÷ 45

Divide numerator and denominator by 15:

> 1320 ÷ 15 = 88
> 45 ÷ 15 = 3
> So, 88 ÷ 3 = 29 1/3 miles

✔ Answer: 29 1/3 miles (or approximately 29.33 miles)

*(Alternative method: Since 120 minutes is 120/45 = 8/3 times longer than 45 minutes, multiply distance by 8/3: 11 × 8/3 = 88/3 = 29 1/3 miles.)*

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Problem 4:

> A train travels from Chicago, IL to Los Angeles, CA in 1 day and 15 minutes. The distance between the two cities is 2,015.3 miles. How fast was the train going on average?

Solution:

Average speed = Total distance ÷ Total time

First, convert total time to hours.

> 1 day = 24 hours
> 15 minutes = 15/60 = 0.25 hours
> Total time = 24 + 0.25 = 24.25 hours

Now divide distance by time:

> Speed = 2,015.3 miles ÷ 24.25 hours

Let’s calculate:

> 2,015.3 ÷ 24.25

To make it easier, multiply numerator and denominator by 100 to eliminate decimals:

> 201,530 ÷ 2,425

Do the division:

> 2,425 × 83 = 2,425 × 80 + 2,425 × 3 = 194,000 + 7,275 = 201,275
> 201,530 - 201,275 = 255
> So, 83 + 255/2425 ≈ 83.105...

So, approximately 83.1 miles per hour

✔ Answer: 83.1 miles per hour (rounded to one decimal place)

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✔ Final Answers:

1. $2.25
2. 32 eggs
3. 29 1/3 miles (or 29.33 miles)
4. 83.1 miles per hour

Let me know if you’d like to see any part explained differently!