Combined Rates

Calculate how long tasks take when multiple workers or machines work together.

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Calculate how long tasks take when multiple workers or machines work together.

When multiple workers or machines work together, their rates add up. If Machine A produces 5 units/hour and Machine B produces 3 units/hour, together they produce 8 units/hour. To find time for a task, divide the total work by the combined rate. This also applies to pipes filling tanks or people completing tasks.

Combined Rate = Rate A + Rate B. Time = Total Work / Combined Rate

A makes 4/hr, B makes 6/hr → Together 10/hr → 50 units take 5 hours
Pipe A fills in 6 hrs, B in 3 hrs → Rates: 1/6 + 1/3 = 1/2 → Together: 2 hours
Worker A: 8 items/day, B: 12 items/day → 100 items = 100/20 = 5 days together

How to recognize it

Multiple workers/machines working simultaneously
Individual rates are given (units per time)
Asked for time when working together

Common mistakes

Averaging rates instead of adding them
Adding times instead of rates (if A takes 2hr and B takes 3hr, together is NOT 5hr)
Forgetting to convert to consistent rate units

Step-by-step walkthrough

Pipe A can fill a tank in 4 hours. Pipe B can fill the same tank in 6 hours. How long to fill the tank using both pipes?

Calculate Pipe A's rate: 1 tank / 4 hours = 1/4 tank per hour
Calculate Pipe B's rate: 1 tank / 6 hours = 1/6 tank per hour
Add the rates: 1/4 + 1/6 = 3/12 + 2/12 = 5/12 tank per hour
Calculate time: 1 tank / (5/12 per hour) = 12/5 = 2.4 hours

Answer: 2.4 hours (or 2 hours 24 minutes)

Practice guidance

Numerical Reasoning