Nicholas's sand castle is 30 cm tall and he is adding sand at a rate of 12 cm per minute. Nina's sand castle is 78 cm tall and she is adding more sand to it at a rate of 6 cm per minute. After how many minutes, x, will Nina and Nicholas's sand castles be the same height?

8 minutes

Step-by-step explanation:

Speed or Rate = Distance / time

Distance = Speed × time

Nicholas's sand castle is 30 cm tall and he is adding sand at a rate of 12 cm per minute.

Nicholas = Nina

30cm + (12cm/min)x

= 30 + 12x

Nina's sand castle is 78 cm tall and she is adding more sand to it at a rate of 6 cm per minute.

78cm + (6cm/min)x

78 + 6x

30 + 12x = 78 + 6x

12x - 6x = 78 - 30

6x = 48

x = 48/6

x = 8 minutes

Therefore, after 8 minutes, Nina and Nicholas's sand castles be the same height.

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