At a bubble-tea stall, two pumps fill an empty rectangular drink dispenser U and an empty cubical drink dispenser V. All the pumped drink stays in the dispensers. Dispenser U measures 24 cm by 50 cm by 100 cm, while each inner side of V measures 40 cm. Pump R is switched on at 10 15 and fills U at 9 litres per minute. After 4 minutes, pump S is switched on and fills V at 8 litres per minute. Both pumps are stopped together. When pump R is stopped, dispenser U is 34 full.
- Find the volume of drink in U, in litres, when pump R is stopped.
- Find the number of minutes for which pump S was switched on.
- Find the depth of the drink in V, in centimetres, when both pumps are stopped.
Need a hint?
Use the 34-full dispenser U to work out how long R ran. Then account for the delay before using S's rate to find the amount of drink in V.
Worked answer
- Volume of U = 24 × 50 × 100 = 120 000 cubic centimetres = 120 litres.
- Drink in U = 120 × 34 = 90 litres.
- Pump R ran for 90 ÷ 9 = 10 minutes.
- Pump S ran for 10 − 4 = 6 minutes.
- Drink pumped into V = 6 × 8 = 48 litres.
- Capacity of V = 40 × 40 × 40 = 64 000 cubic centimetres = 64 litres.
- Fraction of V filled = 48 ÷ 64 = 34.
- Depth of drink = 34 × 40 = 30 cm.
The mistake this question tests
Minutes and hours in rate
The usual wrong path is to ignore the 4-minute delay, which makes S run for too long. Some pupils also treat the amount pumped into V as a full cubical dispenser instead of finding its depth.
How to fix it at home →Wrong answers children often give:
- 48 Left out the units
- 50 Minutes and hours in rate
More PSLE rate questions
A tap fills 3 litres of water in 45 seconds
See the answer →Short answer · 2mKara notices that every 6 drops from the loose cap of her sports water bottle together make 5 ml of water
See the answer →Structured · 4mAt 8.00 a.m., a filling machine at Mrs Lim's drink stall began filling empty bottles
See the answer →Structured · 3mTwo printers, Cedar and Maple, each print an identical batch of flyers at a constant rate
See the answer →MCQ · 1mNurul bought 5 notebooks for $80
See the answer →Structured · 3mAt a garden centre, 5 points are earned for every $4 spent
See the answer →Practise PSLE rate until the mistakes stop.
Three PSLE questions, free, no sign-up. You’ll see exactly where the marks went. Then 7 days of everything for S$4.99.