Why do the BMR of Rat is higher than an Elephant

Rat eat a Western style breakfast

It is not a proper answer in biological sense

perhaps true but was all I could think of at time

You may have been wrong, but where's the evidence?

the bigger elephant is, the more gravity it will suffer, so usually elephants don't run or do other strenuous activies. They eat a lot every day to make sure that they have enough energy to support their daily activities, but they never sweat because they don't have such a system to control their body temperature, that is why we usually see elephants taking showers in rivers and flapping their big ears on TV because these are only ways to help them feel cool.
But rats, you see they usually eat high energy food and continue doing lots activities, although they nither have a system to sweat, but compared with elephants, they can reduce heat by breathing. In addition, rats usually have nearly 30 to 50 babies in a year because female rats can get pregnants for even 8 times in a whole year, which will lead to more energy loss.
By the way, female elephants usually have their babies after at least 600 days being pregnant and they have to take care of baby elephants for a few years.