The 900-Litre Rainwater Tank
Every year Class 7 of Rupsha High School runs a small plant nursery. This year the school installed a rainwater tank beside the shed. The tank holds 900 litres, and on the first morning of the monsoon week it already contained 300 litres.
The gardeners collect water only from the shed roof, and the week's collection was recorded as: Saturday 180 L, Sunday 240 L, Monday 150 L, Tuesday 300 L, Wednesday 210 L, Thursday 90 L, Friday 330 L.
Every evening, whatever the tank holds, the club drains exactly 120 litres for watering the nursery beds. If a day's collection would push the tank above 900 litres, the extra water spills out of the overflow pipe and is lost; the evening's 120 litres is then taken from the full tank.
On Friday evening the teacher says, 'Next year we will double the tank to 1,800 litres and never lose a drop.'
1. Work out the tank level at the end of each evening and state how much rainwater was lost during the week. Show the level after each morning's collection (before any spilling) as well as after the evening draw.
Read the worked answer
Build the table day by day; the cap must be applied before the evening draw, because spilling happens during collection.
| Day | Start | + collection | Before cap | Lost | After draw |
|---|---|---|---|---|---|
| Sat | 300 | +180 | 480 | 0 | 360 |
| Sun | 360 | +240 | 600 | 0 | 480 |
| Mon | 480 | +150 | 630 | 0 | 510 |
| Tue | 510 | +300 | 810 | 0 | 690 |
| Wed | 690 | +210 | 900 | 0 | 780 |
| Thu | 780 | +90 | 870 | 0 | 750 |
| Fri | 750 | +330 | 1080 | 180 | 780 |
Only Friday spills: 750 + 330 = 1080, which is 180 L more than the tank can hold, so 900 L stays and 180 L leaves through the overflow pipe.
Check: 300 (start) + 1500 (collected) − 180 (lost) − 840 (7 × 120 drawn) = 780 L, which is exactly Friday evening's level. Wednesday reaches 900 L exactly, but 'full' is not 'overflowing', so nothing is lost that day.
2. What is the smallest tank capacity that would have lost no water in this same week? Explain how you know no smaller tank would do.
Read the worked answer
The tank can never lose water unless the level after collection goes above its capacity. Using the uncapped figures, the highest level reached during the week was Friday's 750 + 330 = 1080 L (the next highest is Wednesday's 900 L).
So a tank of 1080 L would just hold Friday's water and lose nothing. Any smaller tank fails: at 1070 L, Friday's collection would spill 10 L; at 1000 L it would spill 80 L.
1080 L is therefore the minimum, because a capacity must be at least the single highest level the tank is asked to hold. Note that the spill happens only on the last day, so capping the tank does not change any of the earlier days' figures and the 1080 L answer is not distorted by the loss itself.
3. The teacher wants to double the tank to 1,800 L so the school will 'never lose a drop'. Judge this plan using the week's data, and state one further piece of information you would want before spending the money.
Read the worked answer
For this particular week the plan works: 1800 L is 720 L above the 1080 L actually needed, so nothing would spill.
But the claim 'never' is not supported by one week of data. The tank failed on exactly one day, the heaviest (330 L), and only by 180 L. A week with two or three days near 330 L, or one day above 400 L, would need a larger tank (or a smaller evening draw) whatever the size chosen from this week's figures.
A sensible rule is that the capacity must exceed (highest single-day collection) + (that evening's draw), because the tank starts the day already partly full.
The further information worth having: the highest single-day collection ever recorded on that roof, taken over several years if possible. Without that number, 1800 L is a guess that happens to fit one lucky week.
One point in the teacher's favour: the tank never fell below 360 L, so a 120 L evening draw is safe even through a short dry spell - the risk here is overflow, not shortage, so money spent on capacity does buy something real.