 # Question

a) Tank X gains 1200cm3 and Tank Y gain 1800cm3 every minute.

Since their respective base areas are (20 x 15 = 300cm3) and (20 x 18 = 360cm3) respectively, this means they will gain (1200 / 300 = 4 cm) and (1800 / 360 = 5 cm) respectively every minute.

Therefore, Tank Y will gain 1 more cm than Tank X every minute. Since Tank X already has 8 cm at the start, this means Tank Y only needs (1 x 8 = 8 min) to overcome that 8 cm lead.

 Time Height in Tank X Height in Tank Y 0 min 8 cm 0 cm 1 min 12 5 2 min 16 10 3 min 20 15 4 min 24 20 5 min 28 25 6 min 32 30 7 min 36 35 8 min 40 40

b) Tank X gains 1200cm3 and Tank Y gain 1800 cm3 every minute.

This means that Tank Y gains (1800 cm3 – 1200 cm3 = 600 cm3) more than Tank X every minute.

Since Tank X already has (15 x 20 x 8 = 2400 cm3) of water at the start, this means that Tank Y only needs (2400 cm3 / 600 cm3 = 4 min) to overcome that 2400 cm3 lead.

 Time Vol in Tank X Vol in Tank Y 0 min 2400 0 1 min 3600 1800 2 min 4800 3600 3 min 6000 5400 4 min 7200 7200
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