Time & Work Kit for School Maths Lab

Quick Answer: The Time & Work Kit is a maths lab resource for modelling time-and-work problems, in which a whole job is treated as one unit and each worker completes a fraction of it per day or per hour. Secondary classes use the time and work kit for combined-work, person-days and pipes-and-cisterns problems.

Treating the Job as One Whole

Time-and-work problems become easier once the job is pictured as a whole split into equal parts. If A can paint a wall in 6 days, A paints 1/6 of it each day; if B takes 3 days, B paints 1/3. A model that shows the job as a strip, board or tank divided into sixths lets students shade A’s share and B’s share for one day together, see that half the wall is done, and conclude that the pair need 2 days.

The same picture handles inverse proportion. If 4 workers need 6 days, the job amounts to 24 person-days, so 8 workers need 3 days, and a job drawn as 24 equal blocks shows why doubling the workers halves the time. Pipes-and-cisterns questions work the same way, with a filling pipe counted as positive work and an emptying pipe as negative work.

Kits sold under this name differ in form, from fraction strips and boards to model tanks, so confirm the contents before planning lessons around a particular activity.

Applications

• Shading one day’s work for two or three workers and finding the time they take together
• Showing why more workers finish sooner, using a fixed number of person-days
• Modelling a tank filled by one pipe while another pipe empties it
• Checking the LCM method, where the job is taken as the LCM of the given times

Specifications

Care & Handling

• Keep the pieces of the time and work kit sorted by the fraction they represent, so a full set of sixths or eighths is ready when needed.
• Wipe boards or strips with a dry cloth; if any part takes markers, use dry-wipe markers only.
• Store the kit flat in a dry cupboard to prevent warping.

Why Choose LabEquip

Teachers who use a kit like this usually want students to stop memorising formulas and see a job as fractions of a whole. It sits with other number and proportion resources in the Mathematics School Lab Products range, and the Fraction Bar helps learners who first need confidence with unit fractions. Ask about contents through the contact page.

Frequently Asked Questions

What is the unit method for time and work problems?

Treat the whole job as 1. A worker who takes n days completes 1/n of the job per day. Add the daily fractions for people working together, then divide 1 by the total to find the number of days.

How long do A and B take together if A takes 10 days and B takes 15 days?

A does 1/10 and B does 1/15 of the job per day. Together that is 3/30 plus 2/30, or 5/30, which simplifies to 1/6. So they finish in 6 days, fewer than either needs alone, as expected.

What is the LCM method?

Take the total work as the lowest common multiple of the given times, for example 30 units when the times are 10 and 15 days. A then does 3 units a day and B 2 units, so together they do 5 units a day, and 30 divided by 5 gives 6 days. It avoids fractions for students who find them difficult.

How are pipes and cisterns related to time and work?

Filling a tank is a job just like painting a wall. A filling pipe adds a fraction of the tank per hour, while a leak or outlet pipe removes a fraction. The net rate is the sum, with outlets counted as negative.

Why is time inversely proportional to the number of workers?

When the total work is fixed, the number of workers multiplied by the number of days stays the same. Doubling the workers halves the days, provided everyone works at the same rate. This is the idea behind person-days.

Which classes use a time and work kit?

It is used in middle and secondary school arithmetic and is also useful when revising for aptitude and entrance tests, where time-and-work and pipes-and-cisterns questions appear often.

Last Updated: September 2026