# Precalculus ?

George and Paula are running around a circular track. George starts at the westernmost point of the track, and Paula starts at the easternmost point. The illustration below shows their starting positions and running directions. They start running toward each other at constant speeds. George runs at 6 feet per second. Paula takes 40 seconds to run a lap of the track. George and Paula pass each other after 13 seconds.

How would I go about solving for this problem?

How would I determine how far east of his starting point is George after running for 3 minutes (in ft)? (Round your answer to three decimal places .)

### 2 Answers

- 1 month ago
The period of Paula’ track is 40 seconds, and she takes 13 seconds to meet George for the first time.

40*50%-13 = 7 seconds for Paula to reach George’ starting point after their meeting.

George run 78 ft in 13 seconds

Paula runs 78 ft in 7 seconds

Full circle in feet is

78/(7/40) = 445.714

George runs 6 ft per second.

6*60*3 = 1080 ft in 3 minutes

Because George’ started from west. Substract half circle rans in degrees and take it’s Cosine, then multiply the ratio of feet/radian

Cos( (1080/445.714-0.5) *360) * ( 445.714/ (2pi) ) = 62.812 ft east