The useful life of a certain piece of equipment

[mattlestarge]

The useful life of a certain piece of equipment is determined by the following formula: u =(8d)/h2, where u is the useful life of the equipment, in years, d is the density of the underlying material, in g/cm3, and h is the number of hours of daily usage of the equipment. If the density of the underlying material is doubled and the daily usage of the equipment is halved, what will be the percentage increase in the useful life of the equipment?

The answer to this question is 700% if numbers are chosen greater than 1 . But when i did the problem I used 1 and 1 for the values of d and h originally and then when I use 2 and 1/2 respectively, the answer seems to be 800% increase not 700%

Should I use the term "h is the number of hours" where hours is plural to understand that it must be more than 1 hour originally ? 2 hours minimum ? That seems like semantics to me, a trick with words. Should it not specify that constraint? Or am i simply making a careless math error ?

[mattlestarge]

Nevermind I see that i did the percentage wrong.

[jnelson0612]

Nevermind I see that i did the percentage wrong.

Great! Always best to see your own mistakes. :-)

[pnf619]

The division sign u = 8d/h^2 in the original question that shows up in the CAT isn't very clear. some might think its an additional variable.

[RonPurewal]

The division sign u = 8d/h^2 in the original question that shows up in the CAT isn't very clear. some might think its an additional variable.

even if that thought were to occur to you, you could dismiss it immediately.
if there were an "additional variable" in the problem, it would have to be defined in the problem, alongside the definitions of u, d, and h.
nothing else is defined in the problem, so, there you go.

[tim]

what variable do you think it would be? in other words, what would you call it?