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If you mow 400 yards for $30 a yard, you will earn 400 * $30 = $<<400*30=12000>>12,000 per week.
If you mow 1 time a week for 4 months, you will earn $12,000 * 4 = $<<12000*4=48000>>48,000 in total.
If you split the money 50/50 with your sister, you will each receive $48,000 / 2 = $<<48000/2=24000>>24,000. Answer: \boxed{24000}.