GMAT rates strategies
Rates and work problems come down to one principle: rates add, times do not. These strategies cover the core formula, the rate table for multi-phase problems, the most common trap the answer choices are built around, and a worked example you can follow step by step.
The core formula
Rate equals work divided by time. Time equals work divided by rate. Every rates question on the GMAT starts from this relationship. If a crew installs 3 beams per day and needs to install 24 beams, the time is 24 divided by 3, which is 8 days. If a machine fills a tank in 6 hours, its rate is one-sixth of the tank per hour.
Rates add, times do not
Machine A fills a tank in 6 hours. Machine B fills the same tank in 3 hours. How long do they take together? The instinct is to average the times: (6 plus 3) divided by 2 equals 4.5 hours. That is wrong. Convert each time to a rate. Machine A fills one-sixth of the tank per hour. Machine B fills one-third of the tank per hour. Together they fill one-sixth plus one-third, which is one-half of the tank per hour. At that combined rate, the full tank takes 2 hours. The rule: convert each worker's time to a rate (one job divided by their solo time), add the rates, then convert back to time (one job divided by the combined rate). Never add or average the times.
The rate table for multi-phase problems
When a problem has head starts, pauses, or staggered schedules, build a table with one row per phase: | Phase | Rate | Time | Work | |---|---|---|---| | A alone | 1/6 per hour | 2 hours | 2/6 = 1/3 | | A + B together | 1/2 per hour | ? hours | 2/3 remaining | Machine A works alone for 2 hours and completes one-third of the job. The remaining two-thirds is covered by A and B together at a combined rate of one-half per hour. Time equals two-thirds divided by one-half, which is four-thirds hours. The table keeps the arithmetic organized. Each row is one phase. The work column always sums to 1 (the whole job). Fill in what you know, solve for what you do not.
The most common trap
Averaging the times instead of adding the rates
Averaging two completion times gives a number that looks reasonable but has no mathematical basis. The answer choices include the average because the test writers know this mistake. Always convert to rates first, add the rates, then convert back.
Step-by-step strategy
When to use: any question about two or more workers, machines, or pipes completing a job together.
- 1Write each worker's rate as 1 divided by their solo completion time.
- 2Add the rates of all workers who are active simultaneously.
- 3Divide 1 by the combined rate to get the together-time.
- 4For multi-phase problems, build a table and track the remaining work.
When not to use: when the question gives rates directly (no conversion needed), or when only one worker is involved.
Worked example
A farmer can harvest a field in 6 hours using a tractor. A second tractor, which is slower, can harvest the same field in 8 hours. If both tractors work together for 2 hours, what fraction of the field remains unharvested? Step 1: Convert each tractor's time to a rate. The first tractor harvests one-sixth of the field per hour. The second harvests one-eighth per hour. Step 2: Add the rates. One-sixth plus one-eighth equals seven-twenty-fourths per hour. Step 3: Multiply by the time worked. Seven-twenty-fourths times 2 hours equals seven-twelfths of the field harvested. Step 4: Subtract from the whole. One minus seven-twelfths equals five-twelfths. The answer is five-twelfths.
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