Carmen and Susan are members of their school’s running club. The length of the circular track at the school is 1/10 of a mile.


In the time it takes Carmen to run 3 times around the track, Susan runs 4 times around the track.

A. In the time it takes Carmen to run 12 times around the track, how many times could Susan have run around the track? Show your work or explain how you know.

Carmen and Susan both run 1 mile. They start at the same time.

B. When Susan finishes, how many times does Carmen still have to run around the track? Show your work or explain how you know.

A.

for Carmen to run 3 times, Susan runs 4 times around the track
for Carmen to run 1 times, Susan runs 4/3 around
for Carmen to run 12 times, Susan runs 12(4/3) or 16 times around the track
(notice that this is a straight ratio thing)

16

A. To find out how many times Susan could have run around the track in the time it takes Carmen to run 12 times around the track, we can set up a proportion based on the given information.

Since Susan runs 4 times around the track while Carmen runs 3 times around the track, we can write the proportion as:

(Carmen's runs) : (Susan's runs) = 3 : 4

Now, we can solve for Susan's runs by cross-multiplying:

(Carmen's runs) * 4 = (Susan's runs) * 3

12 * 4 = (Susan's runs) * 3

48 = (Susan's runs) * 3

(Susan's runs) = 48 / 3

(Susan's runs) = 16

Therefore, in the time it takes Carmen to run 12 times around the track, Susan could have run around the track 16 times.

B. Since both Carmen and Susan run 1 mile, and the length of the circular track is 1/10 of a mile, Carmen needs to run 10 laps to complete 1 mile. Therefore, when Susan finishes running 1 mile, Carmen still has to run 10 - 3 = 7 more laps around the track.

Carmen still has to run around the track 7 times.