Primary Maths Water Tanks: Separate the Stages Before Combining Rates

A learner asking for help with a Singapore Primary 6 water-tank problem received an important correction: the outlet started later than the inlet. The arithmetic had to follow that sequence. The public homework discussion also highlighted mixed units and the difference between additional time and total time. Here is a fresh worked example that makes those decisions visible.

Draw a timeline before choosing an operation

Write the starting event on the left and the next change in the middle. Under each interval, record which taps are running. A tap mentioned in the question does not necessarily operate throughout the whole story. Words such as “after”, “then” and “another” tell you where one stage ends and the next begins.

For each interval, ask what happens to the water already in the tank. Does it stay there? Does an outlet remove some of it? Is the tank emptied before the next stage? This short explanation is more useful than immediately searching for a formula containing every number.

The MOE Primary Mathematics syllabus includes cuboid volume and the relationship between millilitres and cubic centimetres. Those connections let a child translate a required water height into an amount of water. In the example below, all dimensions are internal measurements and the stated flow rates remain constant.

Work through an original two-stage example

An initially empty rectangular tank has a base measuring 30 cm by 20 cm. An inlet supplies 900 ml of water each minute. After four minutes, an outlet is opened and removes 300 ml each minute while the inlet continues running. How long after the inlet starts will the water first reach a height of 18 cm?

First find the target volume. The base area is 30 × 20 = 600 cm², so the required water volume is 600 × 18 = 10,800 cm³. Since 1 cm³ corresponds to 1 ml, the target is 10,800 ml. Label this as the target, rather than the amount still needed.

During the first four minutes, only the inlet operates. The water collected is 900 × 4 = 3,600 ml. The second stage therefore needs another 10,800 − 3,600 = 7,200 ml. It would be incorrect to start this stage with an empty tank.

Once both taps operate, each minute adds 900 ml and removes 300 ml. The net increase is 600 ml per minute. The additional time is 7,200 ÷ 600 = 12 minutes. The question measures time from the inlet starting, so the answer is 4 + 12 = 16 minutes.

Check the answer by rebuilding the story

Use a different calculation to check the result. Over 16 minutes the inlet supplies 16 × 900 = 14,400 ml. The outlet runs for only 12 minutes, removing 12 × 300 = 3,600 ml. The amount left is 14,400 − 3,600 = 10,800 ml, exactly the target.

A height check gives another useful interpretation. At the four-minute mark, the height is 3,600 ÷ 600 = 6 cm. During the second stage the height rises by 600 ÷ 600 = 1 cm each minute. Twelve more minutes therefore take it from 6 cm to 18 cm.

Handle variations without memorising another rule

If the outlet is faster than the inlet, subtracting the rates produces a decrease. A target above the current level cannot then be reached during that stage. If the target was reached before the outlet opened, stop in the first stage instead. Checking the target against the amount at the changeover prevents an unnecessary second calculation.

If one rate is given in litres per minute and the other in millilitres per minute, convert them before subtracting. For example, 0.3 litres per minute is 300 ml per minute. Write the unit beside the converted number; subtracting 900 and 0.3 directly would mix quantities measured on different scales.

Practise the reading decision

Choose a suitable upper-primary question from the Primary Maths collection. Before solving, annotate the start of every tap and underline the event from which time is measured. After checking the solution, change just the outlet's starting time and explain which lines of working must change. This turns one question into practice in reading a sequence, rather than copying a familiar subtraction.