Rate Word Problems - Teach-nology - Free Printable

Let's solve each of the rate word problems step by step and explain the reasoning.

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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?

#### Step 1: Find the price per can
We divide the total cost by the number of cans:
$$
\text{Price per can} = \frac{56.25}{75} = 0.75
$$
So, each can costs $0.75.

#### Step 2: Multiply by 3 cans
$$
3 \times 0.75 = 2.25
$$

✔ Answer: Nathan would have to pay $2.25 for 3 cans.

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Problem 2:

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

#### Step 1: Understand the ratio
The recipe uses:
- 4 eggs : 1.5 pounds of flour

We want to find how many eggs are needed for 12 pounds of flour.

#### Step 2: Set up a proportion
$$
\frac{4 \text{ eggs}}{1.5 \text{ lbs}} = \frac{x \text{ eggs}}{12 \text{ lbs}}
$$

Cross-multiply:
$$
4 \times 12 = 1.5x \Rightarrow 48 = 1.5x
$$

Now divide:
$$
x = \frac{48}{1.5} = 32
$$

✔ Answer: You would need 32 eggs.

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Problem 3:

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

#### Step 1: Convert time to the same unit
2 hours = 120 minutes

#### Step 2: Find her rate (miles per minute)
$$
\text{Rate} = \frac{11 \text{ miles}}{45 \text{ minutes}} = \frac{11}{45} \approx 0.2444 \text{ miles per minute}
$$

#### Step 3: Multiply by 120 minutes
$$
\text{Distance} = \frac{11}{45} \times 120 = \frac{1320}{45} = 29.\overline{3} \approx 29.33 \text{ miles}
$$

Alternatively, simplify:
$$
\frac{11}{45} \times 120 = 11 \times \frac{120}{45} = 11 \times \frac{8}{3} = \frac{88}{3} = 29\frac{1}{3}
$$

✔ Answer: She would travel 29⅓ miles (or 29.33 miles) in 2 hours.

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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?

#### Step 1: Convert time to hours
- 1 day = 24 hours
- 15 minutes = 15/60 = 0.25 hours
- Total time = 24 + 0.25 = 24.25 hours

#### Step 2: Use the formula for average speed
$$
\text{Average speed} = \frac{\text{Distance}}{\text{Time}} = \frac{2015.3}{24.25}
$$

Now divide:
$$
\frac{2015.3}{24.25} = 83.1 \text{ mph}
$$

✔ Answer: The train was going at an average speed of 83.1 miles per hour.

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✔ Final Answers:

1. $2.25
2. 32 eggs
3. 29⅓ miles (or 29.33 miles)
4. 83.1 mph

Let me know if you'd like these explained in simpler terms or with visual models!