Speed and Distance Word Problems worksheet with illustrated examples for calculating distance, speed, and time.

Problem: Speed and Distance Word Problems

We will solve each problem step by step using the formula for distance, speed, and time:
$$
\text{Distance} = \text{Speed} \times \text{Time}
$$
where:
- Speed is in miles per hour (mph),
- Time is in hours,
- Distance is in miles.

If the time is given in minutes, we convert it to hours by dividing by 60 (since 1 hour = 60 minutes).

---

Problem 1:

Yesterday I drove 150 minutes at a speed of 100 miles/h. How many miles did I drive?

#### Step 1: Convert time from minutes to hours.
$$
\text{Time in hours} = \frac{\text{Time in minutes}}{60} = \frac{150}{60} = 2.5 \text{ hours}
$$

#### Step 2: Use the formula for distance.
$$
\text{Distance} = \text{Speed} \times \text{Time} = 100 \times 2.5 = 250 \text{ miles}
$$

#### Final Answer:
$$
\boxed{250}
$$

---

Problem 2:

A bird can fly at a speed of 50 miles/h. If the bird flies for 90 minutes, what distance will it have flown?

#### Step 1: Convert time from minutes to hours.
$$
\text{Time in hours} = \frac{\text{Time in minutes}}{60} = \frac{90}{60} = 1.5 \text{ hours}
$$

#### Step 2: Use the formula for distance.
$$
\text{Distance} = \text{Speed} \times \text{Time} = 50 \times 1.5 = 75 \text{ miles}
$$

#### Final Answer:
$$
\boxed{75}
$$

---

Problem 3:

I usually walk at a speed of 0.75 miles per 30 minutes. How long will it take me to walk from my house to the supermarket 1.5 miles down the road?

#### Step 1: Determine the walking speed in miles per hour.
Since 0.75 miles are covered in 30 minutes, we convert this to miles per hour:
$$
\text{Speed} = \frac{0.75 \text{ miles}}{0.5 \text{ hours}} = 1.5 \text{ miles/hour}
$$

#### Step 2: Use the formula for time.
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{1.5 \text{ miles}}{1.5 \text{ miles/hour}} = 1 \text{ hour}
$$

#### Final Answer:
$$
\boxed{1}
$$

---

Problem 4:

Yesterday I ran 9.6 miles at an average speed of 0.4 miles per 5 minutes. How long did it take me to run 9.6 miles?

#### Step 1: Determine the running speed in miles per hour.
Since 0.4 miles are covered in 5 minutes, we convert this to miles per hour:
$$
\text{Speed} = \frac{0.4 \text{ miles}}{\frac{5}{60} \text{ hours}} = \frac{0.4 \times 60}{5} = 4.8 \text{ miles/hour}
$$

#### Step 2: Use the formula for time.
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{9.6 \text{ miles}}{4.8 \text{ miles/hour}} = 2 \text{ hours}
$$

#### Final Answer:
$$
\boxed{2}
$$

---

Problem 5:

The distance between 2 cities is 7,200 miles. How long will it take a plane that flies at 600 miles/h to travel between the 2 cities?

#### Step 1: Use the formula for time.
$$
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{7200 \text{ miles}}{600 \text{ miles/hour}} = 12 \text{ hours}
$$

#### Final Answer:
$$
\boxed{12}
$$

---

Problem 6:

The distance between my house and my school is 8 miles and takes 10 minutes by bus. How fast is the bus?

#### Step 1: Convert time from minutes to hours.
$$
\text{Time in hours} = \frac{\text{Time in minutes}}{60} = \frac{10}{60} = \frac{1}{6} \text{ hours}
$$

#### Step 2: Use the formula for speed.
$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{8 \text{ miles}}{\frac{1}{6} \text{ hours}} = 8 \times 6 = 48 \text{ miles/hour}
$$

#### Final Answer:
$$
\boxed{48}
$$

---

Final Answers:

1. $\boxed{250}$
2. $\boxed{75}$
3. $\boxed{1}$
4. $\boxed{2}$
5. $\boxed{12}$
6. $\boxed{48}$