Compose equation, simplify and solve

Question

It takes Greg 8.3 min to jog around a track. It takes Tess 12.7 min to jog around the same track. If they start jogging at the same place and time, when and where on the track Tess will see that Greg is side by side with him? What additional distance compared to Tess should Greg jog for being side by side with Tess? Compose equation with the length of track, simplify and solve it. Explain solution.

Answer 1

The trick here is that both Greg and Tess will run the same amount of time.

APPROXIMATELY Greg will run 3 laps while Tess runs 2.

Let's call Tess's distance 1 + x, where x will represent a part of a lap.

Then Greg's distance will be 2 + x because he must "lap" her.

Tess's rate is 1 lap/12.7 min and Greg's is 1 lap/8.3 min.

Time = Distance/Rate.

 

(2+x)/(1/8.3) = (1 + x)/(1.12.7)

16.3 + 8.3x = 12.7 + 12.7x

4.4x = 3.9

x = .886364...this is the part of a 2nd lap which Tess runs before Greg catches up.

 

In total Tess runs 1.886364 laps and Greg runs 2.886364 laps and Greg runs 1 entire lap more than Tess.

 

Check: Tess runs 12.7 * 1.886364 min and Greg runs 8.3 * 2.886364 min

12.7 * 1.886364 = 23.95682 minutes and 8.3 * 2.886364 = 23.95682 minutes as required.