Consider the formula that relates distance, velocity, and time \((d = vt)\).

If you are interested in the time it takes for a ladybug traveling at a speed of 3 inches per second to crawl up a 10-foot section of wall, which unit conversion makes the most sense to use?

A. Converting feet to inches by dividing 10 feet by \(\frac{12 \text{ inches}}{1 \text{ foot}}\)
B. Converting feet to inches by multiplying 11 feet by \(\frac{1 \text{ foot}}{12 \text{ inches}}\)
C. Converting feet to inches by multiplying 10 feet by 12
D. Converting feet to inches by multiplying 10 feet by \(\frac{12 \text{ inches}}{1 \text{ foot}}\)

1 answer

To solve the problem, we need to convert the distance from feet to inches, since the speed of the ladybug is given in inches per second.

  1. We start with the distance: 10 feet.
  2. We know that 1 foot is equal to 12 inches.

To convert 10 feet to inches, we would multiply 10 feet by the conversion factor \(\frac{12 \text{ inches}}{1 \text{ foot}}\):

\[ 10 \text{ feet} \times \frac{12 \text{ inches}}{1 \text{ foot}} = 120 \text{ inches} \]

Now, let's examine the answer choices given:

A. Converting feet to inches by dividing 10 feet by \(\frac{12 \text{ inches}}{1 \text{ foot}}\)
B. Converting feet to inches by multiplying 11 feet by \(\frac{1 \text{ foot}}{12 \text{ inches}}\)
C. Converting feet to inches by multiplying 10 feet by 12
D. Converting feet to inches by multiplying 10 feet by \(\frac{12 \text{ inches}}{1 \text{ foot}}\)

The correct unit conversion that makes the most sense is: D. Converting feet to inches by multiplying 10 feet by \(\frac{12 \text{ inches}}{1 \text{ foot}}\)

This option correctly applies the conversion factor to convert feet into inches.