The School Garden Water Roster
A Year 7 class has a rectangular garden bed 6 m long and 2.5 m wide. They must keep the soil moist for 14 days using only two 200-litre rain tanks. A full watering of the whole bed uses 45 litres. The class agrees on three rules: (1) every part of the bed gets watered on days 1, 7 and 14; (2) on all other days only half the bed's area is watered, alternating which half; (3) the tanks must not drop below 60 litres total at any time as a safety reserve. On day 1 the tanks hold 340 litres combined. A tap left dripping overnight on day 4 wastes 18 litres before it is noticed. No rain falls.
1. Calculate the total water the plan will consume over the 14 days, and decide whether the reserve rule can be kept. Show your working.
Read the worked answer
Full-water days (1, 7, 14) = 3 days × 45 L = 135 L.
Half-area days = 14 − 3 = 11 days. Half the area uses half the water = 22.5 L per day. 11 × 22.5 = 247.5 L.
Planned total = 135 + 247.5 = 382.5 L.
Add the leak: 382.5 + 18 = 400.5 L consumed.
Available above reserve: start 340 L − 60 L reserve = 280 L usable.
400.5 L needed > 280 L usable, so the reserve rule cannot be kept. The plan is short by 400.5 − 280 = 120.5 L even before allowing for the leak's timing. The class must reduce watering or find more water.
2. The class cannot get more water. Propose the smallest change to the plan that keeps the reserve, and justify it with numbers.
Read the worked answer
We must cut consumption to at most 280 L (usable) minus 18 L (leak) = 262 L of planned watering.
Current planned watering is 382.5 L, so we must save 382.5 − 262 = 120.5 L.
Each half-area day switched to no watering saves 22.5 L. 120.5 ÷ 22.5 ≈ 5.36, so we must drop 6 half-area days (saving 6 × 22.5 = 135 L).
New planned use = 382.5 − 135 = 247.5 L. Add leak = 265.5 L, which is under the 280 L usable limit with 14.5 L to spare.
Dropping only 5 days saves 112.5 L, leaving 382.5 − 112.5 + 18 = 288 L, which breaks the reserve. So 6 days is the smallest whole-day change.
A weaker but valid answer: shorten each half-day watering to two-thirds area, but that is harder to schedule and gives less margin.