Distance Speed Time (A) Worksheet | Printable Maths Worksheets - Free Printable

Problem: Speed and Distance Word Problems

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

If time is given in minutes, we will 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 \( \text{Distance} = \text{Speed} \times \text{Time} \).
\[
\text{Distance} = 100 \text{ mph} \times 2.5 \text{ hours} = 250 \text{ miles}
\]

#### 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 \( \text{Distance} = \text{Speed} \times \text{Time} \).
\[
\text{Distance} = 50 \text{ mph} \times 1.5 \text{ hours} = 75 \text{ miles}
\]

#### 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 30 minutes is half an hour, the speed is:
\[
\text{Speed} = \frac{0.75 \text{ miles}}{0.5 \text{ hours}} = 1.5 \text{ mph}
\]

#### Step 2: Use the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).
\[
\text{Time} = \frac{1.5 \text{ miles}}{1.5 \text{ mph}} = 1 \text{ hour}
\]

#### 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 5 minutes is \(\frac{5}{60} = \frac{1}{12}\) hours, the speed is:
\[
\text{Speed} = \frac{0.4 \text{ miles}}{\frac{1}{12} \text{ hours}} = 0.4 \times 12 = 4.8 \text{ mph}
\]

#### Step 2: Use the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).
\[
\text{Time} = \frac{9.6 \text{ miles}}{4.8 \text{ mph}} = 2 \text{ hours}
\]

#### 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 \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \).
\[
\text{Time} = \frac{7,200 \text{ miles}}{600 \text{ mph}} = 12 \text{ hours}
\]

#### 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 \( \text{Speed} = \frac{\text{Distance}}{\text{Time}} \).
\[
\text{Speed} = \frac{8 \text{ miles}}{\frac{1}{6} \text{ hours}} = 8 \times 6 = 48 \text{ mph}
\]

#### Answer:
\[
\boxed{48}
\]

---

Final Answers:

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