If petrol is expected to get exhausted in 100 years with current usage, if we increase the usage/consumption by 50% how many years will it last?

Question

I know the answer is not 50, by by taking examples I came to conclusion of about 66 years, but I want a mathematical derivation without an example.

Answer 1

Let R = the current rate of consumption. The rate of consumption, R, and the time the petrol lasts, 100 years, vary indirectly, R ¤ 1/100. Increase consumption by 50% to 1.5R:

R/1.5R = x/100

where x is the new amount of time the petrol will last. Solve for x.