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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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