Rt=d question

[yo4561]

Hi my friends,

I have a clarifying question on the rt=d formula.

Let's say I am solving for time in the following made-up example:

(115 cm / 2 sec)(t)=400 cm

I realize that you are supposed to simplify the rate, but when you are trying to isolate to solve for the t, wouldn't the right hand side of the equation be equal to:
t=(400)(2/115) because you take the reciprocal of the rate? I realize that this is a simple algebra question, but I am not sure if rates are treated differently given that you have different units here (cm and seconds).

Many thanks for all of your help and thoughtful responses. You are the BEST MP!

[esledge]

(115 cm / 2 sec)(t)=400 cm

I realize that you are supposed to simplify the rate, but when you are trying to isolate to solve for the t, wouldn't the right hand side of the equation be equal to:
t=(400)(2/115) because you take the reciprocal of the rate? I realize that this is a simple algebra question, but I am not sure if rates are treated differently given that you have different units here (cm and seconds).

You would do exactly that. Showing the units at each step, and how they cancel, might actually help show why:

(115 cm / 2 sec) * (t seconds) = 400 cm
t seconds = 400 cm * (2 sec/115 cm)
t seconds = 400 * (2 sec/115) <-----------------the cm units cancel, leaving only units of seconds, as it should be for t.
t seconds = 800/115 seconds