Consider the formula that relates distance, velocity, and time (d = vt). If you are interested in the time it takes for a snail traveling at a speed of 2 centimeters per second to crawl up a 1-meter section of a wall, which unit conversion makes the most sense to use?

Converting meters to centimeters by dividing 1 meter by 100 centimeters.
Converting meters to centimeters by multiplying 1 meter by 100.
Converting meters to centimeters by multiplying 1 meter by (1 meter)/(100 centimeters)
Converting meters to centimeters by multiplying 1 meter by (100 centimeters)/(1 meter)

***AND did you start first with the distributive property or the multiplication property of equality? Explain your selection. What would have happened if you started with the other strategy?

1 answer

To determine the time it takes for a snail traveling at a speed of 2 centimeters per second to crawl up a 1-meter section of a wall, we need to ensure that the units for distance (d) and velocity (v) are the same. In this case, we should convert the distance from meters to centimeters because the speed is given in centimeters per second.

To convert 1 meter to centimeters, the most straightforward and accurate method is to multiply 1 meter by 100 centimeters. This means we convert the distance as follows:

1 meter × 100 centimeters/meter = 100 centimeters.

Now, we can use the formula \( d = vt \) to solve for time (t):

\[ t = \frac{d}{v} = \frac{100 \text{ centimeters}}{2 \text{ centimeters/second}} = 50 \text{ seconds}. \]

Regarding the second part of your question about strategies for approaching this problem, if you used the distributive property, you wouldn't be directly solving the problem at hand since the distributive property generally applies to expressions containing addition or subtraction.

On the other hand, if you used the multiplication property of equality, you would effectively be maintaining the balance of an equation by multiplying both sides by the same value. In this case, you don't really need to apply either the distributive property or the multiplication property of equality in a traditional sense. Instead, you only need the conversion of units followed by solving the equation.

If you started with the other strategy (i.e., using the distributive property inappropriately), you may have confused the operations needed for solving this problem, which could complicate the solution without benefit. Thus, ensuring that you’re using the correct principles for unit conversion and direct calculation will lead you to the answer more efficiently.