Final answer:
To determine the finish line placement, we calculate that the athletes must run 1 full lap plus an additional 2 3/8 miles on the second lap, totaling 6 3/4 miles.
Step-by-step explanation:
The coach wants the athletes to race 6 3/4 miles and the track is 4 3/8 miles around. To find the distance from the starting point to the finish line, we need to calculate the number of laps and the additional distance they will have to run after completing whole laps.
First, we convert the mixed numbers to improper fractions:
- 6 3/4 miles = (6 × 4 + 3) / 4 = 27/4 miles
- 4 3/8 miles = (4 × 8 + 3) / 8 = 35/8 miles
We then divide the total race distance by the length of the track to find the number of laps:
(27/4) / (35/8) = (27/4) × (8/35) = 54/35 laps
This division shows that the athletes need to run 1 whole lap plus a part of the second lap. To find the fraction of the second lap:
54/35 = 1 + 19/35 laps
Therefore, the athletes will run 1 full lap of 4 3/8 miles and will need to run an additional 19/35 of a lap. To find the additional distance, we multiply 19/35 by the length of 1 lap (35/8 miles):
(19/35) × (35/8) = 19/8 = 2 3/8 miles
The finish line should therefore be 2 3/8 miles from the starting point on the second lap.