This one is tricky to set up.
I have a rather clunky approach . . .
Brooks and Avery are running laps around the outdoor track, in the same direction.
Brooks completes a lap every 78 seconds, while Avery completes a lap every 91 seconds.
Brooks (the faster runner) has just passed Avery.
How much time will it take for Brooks to overtake Avery again?"
We will use: .
Let = distance in one lap (say, in feet).
Brooks' rate is ft/sec.
Avery's rate is ft/sec.
In seconds, Avery runs feet.
In the same seconds, Brooks runs feet,
. . which is feet (one lap) more than Avery's distance.
There is our equation! . . .