Printable primary math worksheet for math grades 1 to 6 based on ... - Free Printable

Let's solve each of these unit rate word problems step by step. A unit rate is a rate where the second quantity is 1 (e.g., miles per hour, emails per day). We'll use proportional reasoning to find the time or amount needed.

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Problem 1:

I write about 12 emails per day. How long will it take me to write 60 emails?

- Given: 12 emails per day
- Find: Time to write 60 emails

Step-by-step:

We can set up a proportion:

$$
\frac{12 \text{ emails}}{1 \text{ day}} = \frac{60 \text{ emails}}{x \text{ days}}
$$

Cross-multiply:

$$
12x = 60
$$

$$
x = \frac{60}{12} = 5
$$

✔ Answer: It will take 5 days.

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Problem 2:

Peter can run 10 kilometers in 2 hours at a steady rate. How long will it take him to run 30 kilometers?

- Given: 10 km in 2 hours → rate = $ \frac{10}{2} = 5 $ km/hour
- Find: Time to run 30 km

Use the formula:

$$
\text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{30}{5} = 6 \text{ hours}
$$

Alternatively, set up a proportion:

$$
\frac{10 \text{ km}}{2 \text{ h}} = \frac{30 \text{ km}}{x \text{ h}}
$$

$$
10x = 60 \Rightarrow x = 6
$$

✔ Answer: It will take 6 hours.

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Problem 3:

I can wash a car in 20 minutes. How long will it take me to wash 20 cars?

- Given: 1 car in 20 minutes
- Find: Time for 20 cars

Since each car takes 20 minutes:

$$
20 \text{ cars} \times 20 \text{ minutes/car} = 400 \text{ minutes}
$$

Convert to hours if needed:

$$
400 \div 60 = 6 \frac{2}{3} \text{ hours} = 6 \text{ hours and } 40 \text{ minutes}
$$

But unless asked, we can leave in minutes.

✔ Answer: It will take 400 minutes (or 6 hours and 40 minutes).

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Problem 4:

I can type 4 words per minute. How long will it take me to write a 500-word essay?

- Given: 4 words per minute
- Find: Time for 500 words

$$
\text{Time} = \frac{500 \text{ words}}{4 \text{ words/minute}} = 125 \text{ minutes}
$$

Convert to hours and minutes:

$$
125 \div 60 = 2 \text{ hours and } 5 \text{ minutes}
$$

✔ Answer: It will take 125 minutes (or 2 hours and 5 minutes).

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Problem 5:

A baker can bake 20 cakes per hour. How long will it take him to bake 400 cakes?

- Given: 20 cakes/hour
- Find: Time for 400 cakes

$$
\text{Time} = \frac{400}{20} = 20 \text{ hours}
$$

✔ Answer: It will take 20 hours.

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Problem 6:

It takes me 10 minutes to swim 2 laps. How long will it take me to swim 5 laps?

- Given: 2 laps in 10 minutes → rate = $ \frac{2}{10} = 0.2 $ laps per minute
- Or better: time per lap = $ \frac{10}{2} = 5 $ minutes per lap

So for 5 laps:

$$
5 \text{ laps} \times 5 \text{ minutes/lap} = 25 \text{ minutes}
$$

Alternatively, set up a proportion:

$$
\frac{2 \text{ laps}}{10 \text{ min}} = \frac{5 \text{ laps}}{x \text{ min}}
$$

$$
2x = 50 \Rightarrow x = 25
$$

✔ Answer: It will take 25 minutes.

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✔ Final Answers Summary:

1. 5 days
2. 6 hours
3. 400 minutes (or 6 h 40 min)
4. 125 minutes (or 2 h 5 min)
5. 20 hours
6. 25 minutes

Let me know if you'd like this formatted as a printable answer sheet!