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

Answer:

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

Step-by-step 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

$h(t) = 100.2 - 10.8t$

$57 = 100.2 - 10.8t$

$10.8t = 43.2$

$t = \frac{43.2}{10.8}$

$t = 4$

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