Speed Time And Distance Worksheet - Fill Online, Printable ... - Free Printable

To solve the problems in the "Speed, Time, and Distance Worksheet," we will use the fundamental relationship between speed, time, and distance:

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

or equivalently,

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

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

We will carefully convert all times to hours (since speeds are given in km/h) and then apply the appropriate formula for each problem.

---

Problem 1a:

Mary rides her bike 43.3 km in 4 hours 20 minutes. What is her average speed in kilometers per hour?

#### Step 1: Convert time to hours
4 hours 20 minutes = \( 4 + \frac{20}{60} \) hours
\[
4 + \frac{20}{60} = 4 + \frac{1}{3} = 4.3333 \, \text{hours}
\]

#### Step 2: Use the formula for speed
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{43.3}{4.3333}
\]

Perform the division:
\[
\text{Speed} \approx 10 \, \text{km/h}
\]

#### Final Answer:
\[
\boxed{10}
\]

---

Problem 1b:

An airplane flies with a constant speed of 1000 km/h. How far can it travel in 17 minutes?

#### Step 1: Convert time to hours
17 minutes = \( \frac{17}{60} \) hours
\[
\frac{17}{60} \approx 0.2833 \, \text{hours}
\]

#### Step 2: Use the formula for distance
\[
\text{Distance} = \text{Speed} \times \text{Time} = 1000 \times 0.2833
\]

Perform the multiplication:
\[
\text{Distance} \approx 283.3 \, \text{km}
\]

#### Final Answer:
\[
\boxed{283.3}
\]

---

Problem 2a:

An airplane flies with a constant speed of 920 km/h. How far can it travel in 1 hour 38 minutes?

#### Step 1: Convert time to hours
1 hour 38 minutes = \( 1 + \frac{38}{60} \) hours
\[
1 + \frac{38}{60} = 1 + 0.6333 = 1.6333 \, \text{hours}
\]

#### Step 2: Use the formula for distance
\[
\text{Distance} = \text{Speed} \times \text{Time} = 920 \times 1.6333
\]

Perform the multiplication:
\[
\text{Distance} \approx 1506.66 \, \text{km}
\]

#### Final Answer:
\[
\boxed{1506.66}
\]

---

Problem 2b:

A van moves with a constant speed of 104 km/h. How long will it take to travel a distance of 422.9 kilometers?

#### Step 1: Use the formula for time
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{422.9}{104}
\]

Perform the division:
\[
\text{Time} \approx 4.0663 \, \text{hours}
\]

#### Step 2: Convert time to hours and minutes
\( 4.0663 \) hours = 4 hours + \( 0.0663 \times 60 \) minutes
\[
0.0663 \times 60 \approx 3.98 \, \text{minutes}
\]

So, the time is approximately 4 hours 4 minutes.

#### Final Answer:
\[
\boxed{4.07}
\]

---

Problem 3a:

A van moves 52 km in 32 minutes. What is its average speed in kilometers per hour?

#### Step 1: Convert time to hours
32 minutes = \( \frac{32}{60} \) hours
\[
\frac{32}{60} = 0.5333 \, \text{hours}
\]

#### Step 2: Use the formula for speed
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{52}{0.5333}
\]

Perform the division:
\[
\text{Speed} \approx 97.5 \, \text{km/h}
\]

#### Final Answer:
\[
\boxed{97.5}
\]

---

Problem 3b:

An airplane flies with a constant speed of 960 km/h. How long will it take to travel a distance of 3552 kilometers?

#### Step 1: Use the formula for time
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{3552}{960}
\]

Perform the division:
\[
\text{Time} = 3.7 \, \text{hours}
\]

#### Final Answer:
\[
\boxed{3.7}
\]

---

Problem 4a:

Noah rides his horse with a constant speed of 11 km/h. How far can he travel in 1 hour 47 minutes?

#### Step 1: Convert time to hours
1 hour 47 minutes = \( 1 + \frac{47}{60} \) hours
\[
1 + \frac{47}{60} = 1 + 0.7833 = 1.7833 \, \text{hours}
\]

#### Step 2: Use the formula for distance
\[
\text{Distance} = \text{Speed} \times \text{Time} = 11 \times 1.7833
\]

Perform the multiplication:
\[
\text{Distance} \approx 19.6163 \, \text{km}
\]

#### Final Answer:
\[
\boxed{19.62}
\]

---

Problem 4b:

An airplane flies with a constant speed of 1000 km/h. How far can it travel in 3 hours 56 minutes?

#### Step 1: Convert time to hours
3 hours 56 minutes = \( 3 + \frac{56}{60} \) hours
\[
3 + \frac{56}{60} = 3 + 0.9333 = 3.9333 \, \text{hours}
\]

#### Step 2: Use the formula for distance
\[
\text{Distance} = \text{Speed} \times \text{Time} = 1000 \times 3.9333
\]

Perform the multiplication:
\[
\text{Distance} \approx 3933.3 \, \text{km}
\]

#### Final Answer:
\[
\boxed{3933.3}
\]

---

Problem 5a:

Noah rides his horse with a constant speed of 16 km/h. How long will he take to travel a distance of 6.7 kilometers?

#### Step 1: Use the formula for time
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{6.7}{16}
\]

Perform the division:
\[
\text{Time} \approx 0.41875 \, \text{hours}
\]

#### Step 2: Convert time to minutes
\( 0.41875 \) hours = \( 0.41875 \times 60 \) minutes
\[
0.41875 \times 60 \approx 25.125 \, \text{minutes}
\]

#### Final Answer:
\[
\boxed{0.42}
\]

---

Problem 5b:

An airplane flies with a constant speed of 800 km/h. How long will it take to travel a distance of 2853.3 kilometers?

#### Step 1: Use the formula for time
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{2853.3}{800}
\]

Perform the division:
\[
\text{Time} \approx 3.5666 \, \text{hours}
\]

#### Final Answer:
\[
\boxed{3.57}
\]

---

Final Answers:

\[
\boxed{10, 283.3, 1506.66, 4.07, 97.5, 3.7, 19.62, 3933.3, 0.42, 3.57}
\]