Question

The time, T (seconds) it takes for a pot of water to boil is inversely proportional to the cooker setting, H ,applied to the pot.

When H=6 T=90.
What must the cooker setting be if it takes 5 minutes to boil the water?

Answer 1

`1.8`

Explanation:

Since the time for the pot of water to boil is inversely proportional to the cooker setting, H, as one goes up, the other must go down:

`T\propto (1)/(H)`

Convert 5 minutes to seconds:

`5\cdot 60=300\:\mathrm{s}`

Therefore, from the initial data given (When H=6, T=90), the new time is
`(300)/(90)=3(1)/(3)` larger. Therefore, H must be
`3(1)/(3)` times smaller for them to be inversely proportional.

`H=(6)/(3(1)/(3))=\boxed{1.8}`