Question

The time it takes to deflate the air out of a spherical balloon is inversely proportional to the rate at which the air is released. The balloon can be deflated in 70 minutes when the air is released at a rate of 400 cubic centimeters per minute. How long will it take to deflate the balloon if the air is released at a rate of 350 cubic centimeters per minute?

Answer 1

70*400=28000
28000/350=80

Therefore 80 minutes is the answer

Answer 2

Time taken = 80 minutes.

Explanation:

The time it takes to deflate the air out of a spherical balloon is inversely proportional to the rate at which the air is released.

Let t be the time to deflate the air out of a spherical balloon and r be the rate at which the air is released.

We have

`t\alpha (1)/(r)`

The balloon can be deflated in 70 minutes when the air is released at a rate of 400 cubic centimeters per minute.

`70\alpha (1)/(400)`

We need to find how long will it take to deflate the balloon if the air is released at a rate of 350 cubic centimeters per minute

`t\alpha (1)/(350)`

Dividing both equations

`(t)/(70)= ((1)/(350))/((1)/(400))\\\\t=80\texttt{minutes}`

Time taken = 80 minutes.