Question
Sammy wants to calculate the time it takes for a ladybug traveling at a speed of 3 inches per second to crawl a distance of 10 feet. Starting with the formula d = rt, Sammy rearranges the formula to highlight time, t, as the quantity of interest. t = d/r
Sammy substitutes the values for rate and time into the formula t = d/r and simplifies to calculate the time. t = 10ft./3 in/sec t = 3.3 sec
Sammy determines it takes the ladybug about 3.3 sec to travel 10ft.
What mistake did Sammy make?
Sammy substitutes the values for rate and time into the formula t = d/r and simplifies to calculate the time. t = 10ft./3 in/sec t = 3.3 sec
Sammy determines it takes the ladybug about 3.3 sec to travel 10ft.
What mistake did Sammy make?
Answers
Answered by
GPT-4o mini
Sammy made a mistake in the calculation of the time taken by the ladybug. Specifically, he did not properly convert the units for distance and speed. Here's the breakdown of the mistake:
1. **Unit Consistency**: The speed of the ladybug is given in inches per second (3 inches/second), while the distance is given in feet (10 feet). To correctly calculate the time, both measurements need to be in the same units.
2. **Conversion**: There are 12 inches in a foot, so 10 feet is equal to \( 10 \times 12 = 120 \) inches.
3. **Using the Formula**: Sammy correctly rearranged the formula to find time:
\[
t = \frac{d}{r}
\]
but he substituted the distance in feet instead of inches.
4. **Calculating with Correct Units**:
\[
t = \frac{120 \text{ inches}}{3 \text{ inches/second}} = 40 \text{ seconds}
\]
Thus, the correct time it takes for the ladybug to travel 10 feet at a speed of 3 inches per second is 40 seconds, not 3.3 seconds.
1. **Unit Consistency**: The speed of the ladybug is given in inches per second (3 inches/second), while the distance is given in feet (10 feet). To correctly calculate the time, both measurements need to be in the same units.
2. **Conversion**: There are 12 inches in a foot, so 10 feet is equal to \( 10 \times 12 = 120 \) inches.
3. **Using the Formula**: Sammy correctly rearranged the formula to find time:
\[
t = \frac{d}{r}
\]
but he substituted the distance in feet instead of inches.
4. **Calculating with Correct Units**:
\[
t = \frac{120 \text{ inches}}{3 \text{ inches/second}} = 40 \text{ seconds}
\]
Thus, the correct time it takes for the ladybug to travel 10 feet at a speed of 3 inches per second is 40 seconds, not 3.3 seconds.