Educational worksheet on calculating velocity, distance, and time with illustrated examples and word problems.

Let's solve each of these problems step by step using the distance, speed, and time relationship:

$$
\text{Speed} = \frac{\text{Distance}}{\text{Time}} \quad \text{or} \quad D = S \times T
$$

We'll use the triangle method (as shown in the image):
- D (Distance) is at the top
- S (Speed) and T (Time) are on the bottom
- To find a variable, cover it in the triangle:
- $ D = S \times T $
- $ S = \frac{D}{T} $
- $ T = \frac{D}{S} $

---

1. What is the velocity of a car that traveled a total of 75 kilometers north in 1.5 hours?

- Distance = 75 km
- Time = 1.5 hr
- Direction = North → velocity includes direction

$$
\text{Velocity} = \frac{75\ \text{km}}{1.5\ \text{hr}} = 50\ \text{km/hr north}
$$

✔ Answer: 50 km/hr north

---

2. What is the velocity of a plane that traveled 3,000 miles from New York to California in 5 hours?

- Distance = 3,000 miles
- Time = 5 hours
- Direction: From NY to CA → westward

$$
\text{Velocity} = \frac{3000\ \text{mi}}{5\ \text{hr}} = 600\ \text{mi/hr west}
$$

✔ Answer: 600 mi/hr west

---

3. John took 45 minutes to bicycle to his grandmother's house, a total of 4 kilometers west. What was his velocity?

- Distance = 4 km
- Time = 45 min
- Direction = West

But we need consistent units. Convert time to hours or keep in minutes.

Let’s convert 45 minutes to hours:
$ 45\ \text{min} = \frac{45}{60} = 0.75\ \text{hr} $

$$
\text{Velocity} = \frac{4\ \text{km}}{0.75\ \text{hr}} = 5.33\ \text{km/hr west}
$$

Alternatively, in km/min:
$ \frac{4\ \text{km}}{45\ \text{min}} = 0.0889\ \text{km/min west} $

But since the options include km/hr, best answer is:

✔ Answer: 5.33 km/hr west

---

4. It took 3.5 hours for a train to travel the distance between two cities at a speed of 120 miles/hour. How many miles lie between the two cities?

- Speed = 120 mi/hr
- Time = 3.5 hr
- Find distance

$$
D = S \times T = 120 \times 3.5 = 420\ \text{miles}
$$

✔ Answer: 420 miles

---

5. How long would it take for a car to travel a distance of 200 km if it is traveling at a speed of 55 km/hr?

- Distance = 200 km
- Speed = 55 km/hr
- Find time

$$
T = \frac{D}{S} = \frac{200}{55} \approx 3.636\ \text{hours}
$$

Convert to hours and minutes:
0.636 × 60 ≈ 38.2 minutes → about 3 hours 38 minutes

But answer should be in hours unless specified.

✔ Answer: 3.64 hours (approximately)

---

6. A car is traveling at 100 km/hr. How many hours will it take to cover a distance of 750 km?

- Speed = 100 km/hr
- Distance = 750 km

$$
T = \frac{750}{100} = 7.5\ \text{hours}
$$

✔ Answer: 7.5 hours

---

7. A plane traveled for about 2.5 hours at a speed of 1200 km/hr. What distance did it travel?

- Speed = 1200 km/hr
- Time = 2.5 hr

$$
D = 1200 \times 2.5 = 3000\ \text{km}
$$

✔ Answer: 3000 km

---

8. A girl is pedaling her bicycle at a speed of 0.10 kilometers/minute. How far will she travel in 120 minutes?

- Speed = 0.10 km/min
- Time = 120 min

$$
D = 0.10 \times 120 = 12\ \text{km}
$$

✔ Answer: 12 km

---

9. An ant carries food at a speed of 1 cm/s. How long will it take the ant to carry a cookie crumb from the kitchen table to the ant hill, a distance of 5000 cm?

- Speed = 1 cm/s
- Distance = 5000 cm

$$
T = \frac{5000}{1} = 5000\ \text{seconds}
$$

✔ Answer: 5000 sec

---

10. The water in the Buffalo River flows at an average speed of 5 km/hr. If you and a friend decide to canoe down the river a distance of 16 kilometers, how many hours will it take?

- Speed = 5 km/hr
- Distance = 16 km

$$
T = \frac{16}{5} = 3.2\ \text{hours}
$$

Or 3 hours and 12 minutes (0.2 × 60 = 12 min)

✔ Answer: 3.2 hours

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## ✔ Final Answers Summary:

| Problem | Answer |
|--------|--------|
| 1 | 50 km/hr north |
| 2 | 600 mi/hr west |
| 3 | 5.33 km/hr west |
| 4 | 420 miles |
| 5 | 3.64 hours |
| 6 | 7.5 hours |
| 7 | 3000 km |
| 8 | 12 km |
| 9 | 5000 sec |
| 10 | 3.2 hours |

Let me know if you'd like these filled into the triangles!