Mathematics
Work and time
Class 8
Intermediate
About 15 min
Premium
Work and time: filling the water tank
Open two taps and a drain on a rooftop water tank and find how long it takes to fill, by adding the work done each hour.
Core concept
If a job takes a hours, 1/a of it is done each hour; rates add when working together and a drain's rate is subtracted
Topic: Work and time
A rooftop water tank has two taps. Tap A alone fills it in 3 hours, so each hour it fills 1/3 of the tank. Tap B alone takes 6 hours, so it fills 1/6 each hour. Together they fill 1/3 + 1/6 = 1/2 of the tank each hour, so the tank is full in 1 ÷ 1/2 = 2 hours. A drain that would empty the full tank in d hours takes away 1/d each hour. This is the same as two people sharing a job: add what each does in one hour, then divide the whole job by that.
What you will learn
- Find the part of a job done in one hour from the time taken.
- Combine rates to find the time taken working together.
- Include a rate that works against the others, such as a leak.
Before you start
- Adding fractions.
Materials
- Two jugs and a bucket with a small hole
Equipment
- A stopwatch
Procedure
- Tap − or + to set how long each tap alone takes, and to open a drain.
- Drag the clock along the time line to watch the tank fill.
- Record taps of 3 h and 6 h together, and two equal taps.
- Record an open drain that slows the filling, and one that stops the tank ever filling.
How this simulation is simplified
- Each tap and the drain flow at a steady rate.