Math worksheet featuring velocity and speed problems with triangle formulas and a cartoon cyclist.

Problem Analysis and Solutions

The problems provided involve basic calculations of velocity, distance, and time using the formula:

\[
\text{Velocity} = \frac{\text{Distance}}{\text{Time}}
\]

or its rearrangements:

\[
\text{Distance} = \text{Velocity} \times \text{Time}
\]
\[
\text{Time} = \frac{\text{Distance}}{\text{Velocity}}
\]

Let's solve each problem step by step.

---

Problem 1:

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

- Given:
- Distance = 75 km
- Time = 1.5 hours

- Formula:
\[
\text{Velocity} = \frac{\text{Distance}}{\text{Time}}
\]

- Calculation:
\[
\text{Velocity} = \frac{75 \, \text{km}}{1.5 \, \text{hr}} = 50 \, \text{km/hr}
\]

- Answer:
\[
\boxed{50 \, \text{km/hr north}}
\]

---

Problem 2:

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

- Given:
- Distance = 3,000 miles
- Time = 5 hours

- Formula:
\[
\text{Velocity} = \frac{\text{Distance}}{\text{Time}}
\]

- Calculation:
\[
\text{Velocity} = \frac{3,000 \, \text{miles}}{5 \, \text{hr}} = 600 \, \text{miles/hr}
\]

- Answer:
\[
\boxed{600 \, \text{miles/hr west}}
\]

---

Problem 3:

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

- Given:
- Distance = 4 km
- Time = 45 minutes

- Convert time to hours:
\[
45 \, \text{minutes} = \frac{45}{60} \, \text{hours} = 0.75 \, \text{hours}
\]

- Formula:
\[
\text{Velocity} = \frac{\text{Distance}}{\text{Time}}
\]

- Calculation:
\[
\text{Velocity} = \frac{4 \, \text{km}}{0.75 \, \text{hr}} = 5.33 \, \text{km/hr}
\]

- Answer:
\[
\boxed{5.33 \, \text{km/hr west}}
\]

---

Problem 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?

- Given:
- Velocity = 120 miles/hr
- Time = 3.5 hours

- Formula:
\[
\text{Distance} = \text{Velocity} \times \text{Time}
\]

- Calculation:
\[
\text{Distance} = 120 \, \text{miles/hr} \times 3.5 \, \text{hr} = 420 \, \text{miles}
\]

- Answer:
\[
\boxed{420 \, \text{miles}}
\]

---

Problem 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?

- Given:
- Distance = 200 km
- Velocity = 55 km/hr

- Formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Velocity}}
\]

- Calculation:
\[
\text{Time} = \frac{200 \, \text{km}}{55 \, \text{km/hr}} \approx 3.64 \, \text{hours}
\]

- Answer:
\[
\boxed{3.64 \, \text{hours}}
\]

---

Problem 6:

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

- Given:
- Distance = 750 km
- Velocity = 100 km/hr

- Formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Velocity}}
\]

- Calculation:
\[
\text{Time} = \frac{750 \, \text{km}}{100 \, \text{km/hr}} = 7.5 \, \text{hours}
\]

- Answer:
\[
\boxed{7.5 \, \text{hours}}
\]

---

Problem 7:

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

- Given:
- Velocity = 1200 km/hr
- Time = 2.5 hours

- Formula:
\[
\text{Distance} = \text{Velocity} \times \text{Time}
\]

- Calculation:
\[
\text{Distance} = 1200 \, \text{km/hr} \times 2.5 \, \text{hr} = 3000 \, \text{km}
\]

- Answer:
\[
\boxed{3000 \, \text{km}}
\]

---

Problem 8:

A girl is pedaling her bicycle at a speed of 10 kilometers/minute. How far will she travel in 120 minutes?

- Given:
- Velocity = 10 km/min
- Time = 120 minutes

- Formula:
\[
\text{Distance} = \text{Velocity} \times \text{Time}
\]

- Calculation:
\[
\text{Distance} = 10 \, \text{km/min} \times 120 \, \text{min} = 1200 \, \text{km}
\]

- Answer:
\[
\boxed{1200 \, \text{km}}
\]

---

Problem 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?

- Given:
- Velocity = 1 cm/s
- Distance = 5000 cm

- Formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Velocity}}
\]

- Calculation:
\[
\text{Time} = \frac{5000 \, \text{cm}}{1 \, \text{cm/s}} = 5000 \, \text{seconds}
\]

- Answer:
\[
\boxed{5000 \, \text{seconds}}
\]

---

Problem 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?

- Given:
- Velocity = 5 km/hr
- Distance = 16 km

- Formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Velocity}}
\]

- Calculation:
\[
\text{Time} = \frac{16 \, \text{km}}{5 \, \text{km/hr}} = 3.2 \, \text{hours}
\]

- Answer:
\[
\boxed{3.2 \, \text{hours}}
\]

---

Final Answers:

1. \(\boxed{50 \, \text{km/hr north}}\)
2. \(\boxed{600 \, \text{miles/hr west}}\)
3. \(\boxed{5.33 \, \text{km/hr west}}\)
4. \(\boxed{420 \, \text{miles}}\)
5. \(\boxed{3.64 \, \text{hours}}\)
6. \(\boxed{7.5 \, \text{hours}}\)
7. \(\boxed{3000 \, \text{km}}\)
8. \(\boxed{1200 \, \text{km}}\)
9. \(\boxed{5000 \, \text{seconds}}\)
10. \(\boxed{3.2 \, \text{hours}}\)