Imagine that you’re studying a species of radioactive particles that, when at rest, have a lifetime of 100 microseconds (a microsecond is $10^{-6}$ seconds). After that, they disintegrate into other particles. When the particles are fired in a stream past you, you notice that the particles live 3 times as long. How fast are the particles traveling?

If these same particles, whose lifetime when at rest is 100 microseconds, are fired past you at $.993c$, what will their lifetimes be from your perspective? (Give your answer to the nearest microsecond.)