Math Problem Statement

Speedy the snail slides 2cm in 2 seconds and then stops to rest for 4 seconds. Speedy then slides another 10 cm in 20 seconds. What is Speedy’s average speed for the entire trip?\

Solution

To calculate Speedy’s average speed for the entire trip, we need to determine the total distance covered and the total time taken.

1. Total Distance Covered:

  • Speedy slides 2 cm in the first segment.
  • Speedy slides 10 cm in the second segment.

Total distance = 2cm+10cm=12cm2 \, \text{cm} + 10 \, \text{cm} = 12 \, \text{cm}

2. Total Time Taken:

  • The time taken to slide the first 2 cm is 2 seconds.
  • Speedy rests for 4 seconds.
  • The time taken to slide the next 10 cm is 20 seconds.

Total time = 2seconds+4seconds+20seconds=26seconds2 \, \text{seconds} + 4 \, \text{seconds} + 20 \, \text{seconds} = 26 \, \text{seconds}

3. Average Speed:

Average speed is given by the formula: Average Speed=Total DistanceTotal Time\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} Substituting the values we found: Average Speed=12cm26seconds0.46cm/second\text{Average Speed} = \frac{12 \, \text{cm}}{26 \, \text{seconds}} \approx 0.46 \, \text{cm/second}

Therefore, Speedy’s average speed for the entire trip is approximately 0.46 cm/second.

Would you like to dive into more details or have any other questions?

Here are some related questions to consider:

  1. What would Speedy's average speed be if he didn't rest?
  2. How would the average speed change if the rest period was doubled?
  3. What is the total time spent moving?
  4. How does the speed during the first segment compare to the second?
  5. How would the average speed be affected if Speedy slid an additional 5 cm in 10 seconds?

Tip: Average speed is often less than the average of individual speeds because of the time spent at slower speeds or resting.

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Math Problem Analysis

Mathematical Concepts

Speed
Distance
Time

Formulas

Average Speed = Total Distance / Total Time

Theorems

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Suitable Grade Level

Grades 4-6