# GMAT Rates and Work: Units Before Equations | topin

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## Build the equation from units rather than remembered keywords

Rate reasoning is an application of the arithmetic and algebra described in GMAC’s current Quant content. The examples in this article are original, and their constant-rate assumptions are stated explicitly. They are intended to teach setup within [Problem Solving](/gmat/quant/problem-solving), not to predict a fixed count of rate questions on the exam.

Quantity = rate × time works because the units cancel appropriately. Kilometres per hour multiplied by hours gives kilometres. Items per minute multiplied by minutes gives items. If your working multiplies kilometres per hour by minutes without conversion, the resulting number may look plausible but has not been calculated in consistent units.

Original question: a printer produces 18 labels per minute at a constant rate. How many labels does it print in 25 seconds? Convert 25 seconds to 25/60 minute, then calculate 18 × 25/60 = 7.5\. If labels must be completed whole items, the prompt needs to specify the discrete production rule; this basic rate calculation gives 7.5 label-equivalents.

That example shows why context matters. A continuous fluid flow can produce a fractional quantity naturally. A count of fully completed labels may require an additional condition. Do not add an unstated rounding rule just because the object is countable; inspect what the question actually asks.

## Add fractions of a job per hour

Original question: two machines complete a divisible production job in six hours and twelve hours respectively, each at a constant rate. Working simultaneously without interference, how long do they take? Their rates are 1/6 and 1/12 job per hour, giving 1/4 job per hour together. One job therefore takes four hours.

Averaging six and twelve gives nine hours, which is not the combined finishing time. Adding them gives eighteen, which is also wrong. Both operations combine durations instead of contributions. A useful direction check is that the joint team should finish faster than either machine alone when both add positive output without interference.

Alternatively, define the job as twelve units. The machines complete two and one units per hour, so together they complete three units per hour; twelve units take four hours. Choosing a convenient divisible workload changes the representation, not the physical relationship. It can make the arithmetic easier to see.

__Original constant-rate work calculations__
| Worker or team                         | Rate                  | Time for one job |
| -------------------------------------- | --------------------- | ---------------- |
| Machine A                              | 1/6 job per hour      | 6 hours          |
| Machine B                              | 1/12 job per hour     | 12 hours         |
| A and B together                       | 1/4 job per hour      | 4 hours          |
| A with an outflow of 1/12 job per hour | 1/12 net job per hour | 12 hours         |

## Split the problem when a worker joins or leaves

Original question: A alone completes a divisible job in six hours; B alone takes twelve. Both rates stay constant. A works alone for two hours, then B joins. How long from the start until the job is finished? A completes 2 × 1/6 = 1/3 of the job first, leaving 2/3.

After B joins, the joint rate is 1/4 job per hour. The remaining 2/3 takes (2/3)/(1/4) = 8/3 hours. Total elapsed time is 2 + 8/3 = 14/3 hours, or four hours forty minutes. The distinction between remaining time and total time is part of the question, not a rounding detail.

Check the result directly. A works 14/3 hours and completes 7/9 of the job. B works 8/3 hours and completes 2/9\. Together those contributions total one. The verification also catches accidentally giving B the first two hours when the story says B joins later.

Use a phase record with columns for duration, active workers, rate and completed work. You rarely need a large table, but the structure prevents one constant joint rate from being applied across a period when the team changed. Our [Two-Part scheduling examples](/articles/gmat-two-part-analysis-scheduling) develop the related habit of keeping different constraints separate.

An alternative phase example has A and B work together for one hour before B leaves. With the six-hour and twelve-hour individual completion times, they finish 1/4 of the job during that hour. A alone completes the remaining 3/4 at 1/6 job per hour, requiring 9/2 hours. Total elapsed time is 11/2 hours, or five hours thirty minutes.

The two phase examples share rates but have different sequences. Their different total times are therefore expected. When reviewing, retain the timeline alongside the numbers; a familiar combined rate can otherwise tempt you to reuse four hours even when the workers are not together for the entire job.

## Use total distance over total time for average speed

Original question: a cyclist travels 30 kilometres at 15 km/h and returns the same distance at 30 km/h. What is the average speed for the round trip? The outbound journey takes two hours and the return takes one. Total distance is 60 kilometres, total time is three hours, so average speed is 20 km/h.

The arithmetic mean 22.5 km/h treats the two speeds as if they occupied equal times. They do not. When distances are equal, the slower journey consumes more time. Write total distance divided by total time instead of memorising a formula whose conditions you may later forget.

For a second original example, travel at 15 km/h for one hour and 30 km/h for one hour. Distances are 15 and 30 kilometres, so 45 kilometres over two hours gives 22.5 km/h. Here the arithmetic mean works because the durations are equal. The two stories use the same speeds but different weights.

The lesson generalises to rates in tables: a simple mean is appropriate only when the weighting supports it. Our [weighted-average guide](/articles/gmat-table-analysis-weighted-averages) explains how different group sizes can reverse a total comparison even when every subgroup looks stronger.

## Translate simultaneous movement and inflow precisely

Original question: two vehicles start 180 kilometres apart and travel towards each other at constant 40 and 50 km/h on the same route. Their separation closes at 90 km/h, so they meet after two hours. Add speeds because both contribute to reducing the separation.

If they travel in the same direction and the faster begins 30 kilometres behind, the catch-up rate is 50 − 40 = 10 km/h, so catching up takes three hours. Subtract because only the speed difference reduces the gap. A diagram or a short separation equation is safer than treating “two vehicles” as a command to add.

For filling and draining, define the sign. A tank fills at 12 litres per minute while a drain removes 5 litres per minute. Net increase is 7 litres per minute while both rates remain constant. To add 140 litres takes 20 minutes. If the drain starts later, split the timeline as in the work example.

Watch for capacity, starting quantity and rate changes. A constant-rate model applies only while its stated conditions hold. If a tank already contains 30 litres and needs to reach 170, use the 140-litre difference, not the full final volume. When the net rate is zero or negative, reaching a larger target is not established by ordinary filling arithmetic.

## Use a short diagnostic that exposes setup mistakes

Try three original checks. A team completes 1/5 of a job per hour; how long for 3/5? Three hours. A car covers 72 kilometres in 48 minutes; what is the speed in km/h? Ninety. Two constant workers take eight and twenty-four hours separately; how long together? Six hours. Write units before checking these answers.

For each miss, identify whether the cause was units, rate addition, phase duration or the requested final quantity. Re-solve with the units visible and then change the values. Repeating the same result is less informative than constructing a fresh equation. Keep the corrected setup short enough to use under timed conditions.

A timed exercise should include problems where addition is wrong, so you cannot solve by recognising a topic label alone. Mix equal-distance and equal-time averages, simultaneous and sequential work, and positive inflow with opposing outflow. The decision is which quantities describe the same interval and what each rate contributes to the target.

topin’s [free full-length GMAT mock](/gmat/practice-test), marked on the official scale, can test that setup habit within a complete sitting. Do not turn a slow correct answer into proof that the skill is finished. Record the time and method, then practise choosing the appropriate equation efficiently on unfamiliar wording.

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## FAQs

Do I add workers’ completion times?

No. Add their work rates when they work together at constant rates without interference, then divide the required work by the combined rate.

Can I choose an easier total workload?

Yes in a proportional divisible-work model. Choosing twelve units instead of one job can simplify fractions without changing the relationship.

When is the average of two speeds correct?

When the speeds apply for equal durations. For general journeys, use total distance divided by total time.

How do I handle someone joining halfway through?

Split the timeline into phases. Calculate work completed before the change, then the time needed for the remainder.

When do I subtract rates?

When contributions oppose each other, such as an outflow against filling or a same-direction catch-up gap. Define the quantity changing before deciding.

## Sources (checked 5 October 2026)

* [mba.com: Quant arithmetic and elementary algebra scope (checked 5 October 2026)](https://www.mba.com/exams/gmat-exam/about/exam-content)
* [mba.com: no calculator in Quant (checked 5 October 2026)](https://support.mba.com/hc/en-us/articles/14076264362907-GMAT-Calculator-and-Scratch-Paper-Note-Taking-Policies)

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