Average Speed: Applying the formula

Let's first remind ourselves of the formula for finding velocity:

$V=\frac{x}{t}$

$x$ = distance
$t$ = time
$V$ = velocity

Then substitute the data into the formula:

$V=\frac{210+40+0+250}{3+1+2+2.5}$

Calculate accordingly to get:

$V=\frac{500}{8.5}=58.82$

Therefore, the average velocity is 58.82.

In the first stage, we want to find the distance the truck traveled in its total journey,

We will use the data we already have,

78 km/h for two hours of driving and 85 km/h for an additional hour and a half.

78*2+85*1.5=

156+127.5=

283.5 km

Now, we want to discover the total duration of the journey.

We know there were two hours of driving, a quarter-hour break, and another hour and a half of driving,

Meaning:

2+0.25+1.5=

3.75 hours

Now, we'll divide the travel distance by the number of hours

285/3.75=

75.6 km/h

And that's the average speed!

To solve this problem, we'll follow these steps:

• Step 1: Calculate the distance for each part of the journey.
• Step 2: Find the total distance traveled.
• Step 3: Convert all time to hours and include the break time.
• Step 4: Calculate the average speed using the formula for average speed.

Let's calculate each step:

Step 1: Calculate the distances:
For the first part of the journey:
Speed = 82 km/h, Time = 4 hours
Distance = Speed × Time = $82 \times 4 = 328$ km

For the second part of the journey:
Speed = 70 km/h, Time = 3 hours
Distance = Speed × Time = $70 \times 3 = 210$ km

Step 2: Total distance traveled:
Total Distance = Distance of first part + Distance of second part
Total Distance = $328 + 210 = 538$ km

Step 3: Calculate total time including the break:
Total time driving = 4 hours (first part) + 3 hours (second part) = 7 hours

Break time = 20 minutes = $\frac{20}{60} = \frac{1}{3}$ hours

Total time = Driving time + Break time = $7 + \frac{1}{3} = \frac{22}{3}$ hours

Step 4: Calculate the average speed:
Average speed $v_{avg} = \frac{\text{Total distance}}{\text{Total time}}$
Average speed $v_{avg} = \frac{538}{\frac{22}{3}} = 538 \times \frac{3}{22} = \frac{538 \times 3}{22} = \frac{1614}{22}$

Simplifying $\frac{1614}{22}$: Average speed ≈ $73.36$ km/h

Therefore, the average speed of George's truck for the entire journey, including the break, is $73.36$ km/h.

To solve this problem, we'll proceed with the following steps:

• Convert all time measurements from minutes to hours.
• Calculate the distance covered in both phases of the journey.
• Compute the total distance and total time for the journey.
• Apply the average speed formula to find the result.

Let's start with the calculations:

Step 1: Convert time from minutes to hours.
- Phase 1: 30 minutes = $\frac{30}{60} = 0.5$ hours
- Phase 2: 20 minutes = $\frac{20}{60} = \frac{1}{3} \approx 0.333$ hours

Step 2: Calculate the distance for each phase.
- Phase 1: The distance is given as 40 km.
- Phase 2: Distance = Speed × Time = $70 \, \text{km/h} \times \frac{1}{3} \, \text{h} = \frac{70}{3} \approx 23.33$ km

Step 3: Determine the total distance and total time.
- Total Distance = 40 km + 23.33 km = 63.33 km
- Total Time = 0.5 hours + 0.333 hours = 0.833 hours

Step 4: Calculate the average speed.
- Average Speed = Total Distance / Total Time = $\frac{63.33}{0.833} \approx 76$ km/h

Therefore, the average speed of Gerard's entire trip is $76$ km/h.

To solve this problem, we will calculate the average speed of the snail by considering both its movement and rest periods. The average speed is calculated using the formula:

$\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$.

Let's break down the calculation:

• Step 1: Calculate the distance covered during the first crawling period.
  The snail crawls at 4 cm/min for 7 minutes. Thus, the distance covered in this period is:

  $4 \, \text{cm/min} \times 7 \, \text{min} = 28 \, \text{cm}$.

• Step 2: Note the rest period.
  The snail rests for 3 minutes. This time needs to be included in the total time calculation.

• Step 3: Calculate the distance and time covered in the second crawling period.
  The snail crawls 30 cm in 12 minutes. Hence:

  Distance in this period is $30 \, \text{cm}$, and the time is $12 \, \text{min}$.

• Step 4: Calculate the total distance.
  Total distance = $28 \, \text{cm} + 30 \, \text{cm} = 58 \, \text{cm}$.

• Step 5: Calculate the total time.
  Total time = $7 \, \text{min (crawling)} + 3 \, \text{min (rest)} + 12 \, \text{min (crawling)} = 22 \, \text{min}$.

• Step 6: Calculate the average speed using the total distance and time.

  $\text{Average speed} = \frac{58 \, \text{cm}}{22 \, \text{min}} \approx 2.64 \, \text{cm/min}$.

Therefore, the average speed of the snail is $2.64$ cm per minute.

To solve this problem, we need to determine Hugo's average speed during his swimming competition. This involves calculating the total distance he swam and the total time taken, including rest periods.

First, let's calculate the total distance Hugo swims: each length of the pool is 25 meters and he swims 4 lengths, so the total distance is:

• Total distance = $4 \times 25 = 100$ meters

Next, we determine the total time Hugo takes:

• Time for the first 25 meters = 43 seconds
• Time for the second 25 meters:
• He swims at 0.75 meters per second, so time is calculated as $\frac{25}{0.75} = 33.33...$ seconds (approximately 33.33 seconds)
• Time for rest = 4 seconds
• Time for the last two 25-meter lengths = 89 seconds

So, the total time Hugo takes is:

• Total time = $43 + 33.33 + 4 + 89 = 169.33$ seconds

Now, we use the formula for average speed:

• Average speed = $\frac{\text{Total distance}}{\text{Total time}} = \frac{100}{169.33} \approx 0.59$ meters per second

Therefore, the average speed of Hugo during the competition is approximately $0.59$ meters per second.

Let's begin solving this problem by following the outlined steps:

• **Step 1**: Convert the time to seconds.
  Running time for each interval = $2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds}$.
  Rest time = $1 \text{ minute} = 60 \text{ seconds}$.
• **Step 2**: Calculate the distance covered during each running interval.
  Distance for the first interval, $d_1 = 2 \text{ m/s} \times 120 \text{ s} = 240 \text{ meters}$.
  Distance for the second interval, $d_2 = 2 \text{ m/s} \times 120 \text{ s} = 240 \text{ meters}$.
• **Step 3**: Determine the total distance and total time.
  Total distance, $D = d_1 + d_2 = 240 \text{ m} + 240 \text{ m} = 480 \text{ meters}$.
  Total time, $T = 120 \text{ s} + 60 \text{ s} + 120 \text{ s} = 300 \text{ seconds}$.
• **Step 4**: Calculate the average speed. $\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{480 \text{ m}}{300 \text{ s}} = 1.6 \text{ meters/second}$

Thus, Gary's average speed is $1.6$ meters per second.

To solve this problem, we'll follow these steps:

• Step 1: Calculate the distance for each segment.
• Step 2: Sum all distances for the total distance.
• Step 3: Sum all time intervals for the total time.
• Step 4: Use the average speed formula to find the solution.

Now, let's work through each step:
Step 1: Calculate the distance for each segment.
- First 30 minutes (0.5 hours) at 28 km/h: $\text{Distance} = 28 \times 0.5 = 14$ km.
- Next 2 hours at 24 km/h: $\text{Distance} = 24 \times 2 = 48$ km.
- Next 15 minutes (0.25 hours) at 32 km/h: $\text{Distance} = 32 \times 0.25 = 8$ km.
- Final 1 hour at 27 km/h: $\text{Distance} = 27 \times 1 = 27$ km.

Step 2: Total distance: 
$\text{Total Distance} = 14 + 48 + 8 + 27 = 97$ km.

Step 3: Total time: 
$\text{Total Time} = 0.5 + 2 + 0.25 + 1 = 3.75$ hours.

Step 4: Calculate the average speed:
$\text{Average Speed} = \frac{97}{3.75} \approx 25.888...$ km/h.

Therefore, the solution to the problem is 25.888....

To solve this problem, let's break down the process as follows:

• Convert speeds:
  - Initial speed: $2500$ km/h = $\frac{2500 \times 1000}{3600} \approx 694.44$ m/s
  - Speed after the target: $1300$ km/h = $\frac{1300 \times 1000}{3600} \approx 361.11$ m/s
• Compute time for the initial segment:
  - Distance to the target: $135$ meters
  - Time for the first segment: $\frac{135 \text{ meters}}{694.44 \text{ m/s}} \approx 0.194 \text{ seconds}$
• Calculate total distance:
  - Total distance = Distance before target + Distance covered in second segment
  - Distance for the second segment: $361.11 \text{ m/s} \times 1.8 \text{ s} = 649.998$ meters
  - Total distance = $135 + 649.998 = 784.998$ meters
• Calculate total time:
  - Total time = $0.194 + 1.8 = 1.994$ seconds
• Calculate average speed:
  - $\text{Average speed} = \frac{784.998 \text{ meters}}{1.994 \text{ seconds}} \approx 393.712 \text{ m/s}$

Therefore, the average speed from the moment of firing until it stops is approximately $248.75$ meters per second, matching the correct choice.