Final answer:
It will take 4 minutes for the hot air balloon to descend from an altitude of 100 1/5 yards to 57 yards, assuming it descends at a steady rate of 10 4/5 yards per minute.
Step-by-step explanation:
To determine how long it will take the hot air balloon to reach an altitude of 57 yards from its current altitude of 100 1/5 yards, we first need to calculate the total descent needed. The descent per minute is given as 10 4/5 yards.
Initial altitude: 100 1/5 yards = 100 + 1/5
= 100.2 yards
Descent per minute: 10 4/5 yards = 10 + 4/5
= 10.8 yards
Next, we calculate the total descent required to reach 57 yards:
Total descent required: 100.2 yards - 57 yards = 43.2 yards
Now, we calculate the time it will take to descend 43.2 yards at a rate of 10.8 yards per minute:
Time to descend: Total descent / Descent per minute = 43.2 yards / 10.8 yards per minute
= 4 minutes
Therefore, it will take 4 minutes for the hot air balloon to reach an altitude of 57 yards.