Let x be a silver that Elias has to polish, it takes him 40 minutes to do this, then you can find how much silver he can polish during 1 minute: [tex] \frac{x}{40} [/tex].
If Niko polish the same amount of silver during 50 minutes, then at 1 minute he polishes [tex] \frac{x}{50} [/tex].
Both boys polish [tex] \frac{x}{40} + \frac{x}{50} = \frac{5x+4x}{200} = \frac{9x}{200} [/tex] during 1 minute. Then they together spend [tex] \dfrac{x}{ \frac{9x}{200} }= \dfrac{200}{9} [/tex] minutes to polish silver.
Answer: [tex] \frac{200}{9} [/tex] minutes.