Distance Time Speed worksheet - Free Printable

To solve these problems, we will use the basic formula for distance, time, and speed:

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

From this, we can derive:
- \(\text{Distance} = \text{Speed} \times \text{Time}\)
- \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\)

Let's solve each problem step by step.

---

Problem 1:

Carlos walks at a speed of \(6 \, \text{km/hr}\). How far will he go in \(3\) hours?

Solution:
\[
\text{Distance} = \text{Speed} \times \text{Time} = 6 \, \text{km/hr} \times 3 \, \text{hr} = 18 \, \text{km}
\]

Answer: \(18 \, \text{km}\)

---

Problem 2:

A jet ski moves at \(120 \, \text{km/hr}\). How far does it travel in a quarter of an hour?

Solution:
A quarter of an hour is \(0.25 \, \text{hours}\).
\[
\text{Distance} = \text{Speed} \times \text{Time} = 120 \, \text{km/hr} \times 0.25 \, \text{hr} = 30 \, \text{km}
\]

Answer: \(30 \, \text{km}\)

---

Problem 3:

At a speed of \(90 \, \text{km/hr}\), how long does it take to travel \(30 \, \text{km}\)?

Solution:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{30 \, \text{km}}{90 \, \text{km/hr}} = \frac{1}{3} \, \text{hr}
\]
Convert \(\frac{1}{3} \, \text{hr}\) to minutes:
\[
\frac{1}{3} \, \text{hr} \times 60 \, \text{min/hr} = 20 \, \text{min}
\]

Answer: \(20 \, \text{minutes}\)

---

Problem 4:

Tatum takes \(3 \, \text{hours}\) to jog \(45 \, \text{km}\). What is his speed?

Solution:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{45 \, \text{km}}{3 \, \text{hr}} = 15 \, \text{km/hr}
\]

Answer: \(15 \, \text{km/hr}\)

---

Problem 5:

At what speed must a cyclist travel to cover a distance of \(90 \, \text{km}\) in \(2 \, \text{hours}\)?

Solution:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{90 \, \text{km}}{2 \, \text{hr}} = 45 \, \text{km/hr}
\]

Answer: \(45 \, \text{km/hr}\)

---

Problem 6:

Walking at a speed of \(14 \, \text{km/hr}\), Ashley takes \(30 \, \text{minutes}\) to walk from home to school. How far is the school from her home?

Solution:
Convert \(30 \, \text{minutes}\) to hours:
\[
30 \, \text{min} = \frac{30}{60} \, \text{hr} = 0.5 \, \text{hr}
\]
\[
\text{Distance} = \text{Speed} \times \text{Time} = 14 \, \text{km/hr} \times 0.5 \, \text{hr} = 7 \, \text{km}
\]

Answer: \(7 \, \text{km}\)

---

Problem 7:

Travelling at \(60 \, \text{km/hr}\), a minivan took \(12 \, \text{minutes}\) to cover a journey. How long is that journey?

Solution:
Convert \(12 \, \text{minutes}\) to hours:
\[
12 \, \text{min} = \frac{12}{60} \, \text{hr} = 0.2 \, \text{hr}
\]
\[
\text{Distance} = \text{Speed} \times \text{Time} = 60 \, \text{km/hr} \times 0.2 \, \text{hr} = 12 \, \text{km}
\]

Answer: \(12 \, \text{km}\)

---

Problem 8:

At what speed must I walk to travel \(8 \, \text{km}\) in \(12 \, \text{minutes}\)?

Solution:
Convert \(12 \, \text{minutes}\) to hours:
\[
12 \, \text{min} = \frac{12}{60} \, \text{hr} = 0.2 \, \text{hr}
\]
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{8 \, \text{km}}{0.2 \, \text{hr}} = 40 \, \text{km/hr}
\]

Answer: \(40 \, \text{km/hr}\)

---

Final Answers:

1. \(18 \, \text{km}\)
2. \(30 \, \text{km}\)
3. \(20 \, \text{minutes}\)
4. \(15 \, \text{km/hr}\)
5. \(45 \, \text{km/hr}\)
6. \(7 \, \text{km}\)
7. \(12 \, \text{km}\)
8. \(40 \, \text{km/hr}\)

\[
\boxed{18, 30, 20, 15, 45, 7, 12, 40}
\]