Question

A hot air balloon is at an altitude of

100 1/5 yards. The balloon's altitude decreases

by 10 4/5 yards every minute. Determine the

number of minutes it will take the balloon to reach an altitude of 57 yards.

Answer 1

It will take 4 minutes for the balloon to reach an altitude of 57 yards.

Explanation:

Initial altitude:

100 1/5 yards = 100 + 0.2 = 100.2 yards.

Decrease per minute:

10 4/5 yards = 10 + 0.8 = 10.8 yards.

So, after t minutes, the height of the ballon is given by:

`h(t) = 100.2 - 10.8t`

Number of minutes it will take the balloon to reach an altitude of 57 yards.

This is t for which
`h(t) = 57`. So

`h(t) = 100.2 - 10.8t`

`57 = 100.2 - 10.8t`

`10.8t = 43.2`

`t = (43.2)/(10.8)`

`t = 4`

It will take 4 minutes for the balloon to reach an altitude of 57 yards.