Work Rate Questions Are EASIER Than You Think (When You Stop Memorizing Formulas)

By EMPOWERgmat on October 8, 2019

Here is a scene I watch every single week. A Test Taker hits a work rate question, grabs the pen and writes 1/A + 1/B = 1/T before reading the last sentence of the prompt. They plug in the numbers, get an answer, see it sitting right there in the choices, click it and move on. It's wrong. The formula was fine. The QUESTION was different.

Work rate questions are the ones about machines, pipes, painters or printers doing a job at a steady speed. They show up in the Quant section, which on Test Day gives you 31 questions in 62 minutes. Most people treat them as a formula to recall. That's the problem. The GMAT writes these questions knowing you memorized a formula, and then it adds a twist the formula can't handle: a machine breaks down, a drain is open, a third worker shows up late.

The formula isn't the enemy. Trusting it blindly is.

That classic formula works for exactly one situation: two workers who start together, finish together and both help the whole time. Change any one of those details and the formula either breaks or, worse, hands you a number that LOOKS right and happens to be one of the wrong answer choices. The GMAT is adaptive question by question, and you can't go back to change an answer, so a confident wrong click is a costly one.

Here's the good news. You don't need a formula at all. You need one question and a few easy numbers.

The one question: how much gets done in ONE hour?

Every work rate question, no matter how it's dressed up, comes down to this: how much of the job does each worker finish in one unit of time? Once you know that, everything else is adding and subtracting.

And here's the move that makes it EASY. Don't call the job "1 job." Pick a size for the job that every given time divides into cleanly. If one machine takes 6 hours and another takes 4 hours, call the job 12 units, since 12 is the smallest number that both 6 and 4 divide into. Now the first machine does 2 units per hour and the second does 3 units per hour. No fractions. No 1/6 + 1/4. Just 2 and 3.

This is TESTing VALUES, the same tactic you should be using all over Quant. You pick a number that makes the math friendly, because the answer to "how long will it take?" doesn't depend on how big the job is. If that feels like cheating, think about what the GMAT is really testing. It isn't checking whether you remember a formula from school. It's checking whether you can think your way to the answer without wasting time.

A long bar split into twelve equal blocks, with two workers side by side, one filling two blocks and the other filling three blocks in the same short stretch of time. — Give the job a size, and each worker's speed becomes a whole number of blocks.

Try it: the machine that quits

This is a Problem Solving question, the kind where you solve and pick from five answer choices. Grab your pad. Don't read the solution until you've committed to an answer.

Try it

Machine A can finish a certain job alone in 6 hours. Machine B can finish the same job alone in 4 hours. The two machines start the job together and work for 2 hours, and then Machine B breaks down. Working alone at its usual rate, how many more hours will Machine A need to finish the job?

Show the answer

Step 1: Notes on paper. A alone: 6 hr. B alone: 4 hr. Together for 2 hr, then A alone. Find: extra hours for A.

Step 2: Pick a job size. 6 and 4 both divide into 12, so the job is 12 units.

Step 3: One hour of work. A does 12 ÷ 6 = 2 units per hour. B does 12 ÷ 4 = 3 units per hour. Together they do 5 units per hour.

Step 4: What's done so far. 2 hours together is 2 × 5 = 10 units. That leaves 12 minus 10 = 2 units.

Step 5: Finish it. A alone does 2 units per hour, so 2 units take 1 hour. The answer is B.

Check it by testing the answer. 10 units together, plus 1 hour of A at 2 units, makes 12 units. The job is done. It works.

The trap. The formula person finds the "together" time: (6 × 4) ÷ (6 + 4) = 24 ÷ 10 = 2.4 hours. Then they subtract the 2 hours already worked and get 0.4 hours, which is 2/5. That's choice A, sitting there waiting for you. It's how long the job would take if B KEPT working. But B broke. The question changed, and the formula didn't notice.

Try it: the tank that leaks

Same idea, nastier twist. This time one of the "workers" is working against you.

Try it

An inlet pipe can fill an empty tank in 4 hours. A drain at the bottom of the tank can empty a full tank in 6 hours. If the tank starts empty and both the inlet and the drain are open, how many hours will it take to fill the tank?

Show the answer

Step 1: Notes on paper. In: 4 hr to fill. Out: 6 hr to empty. Start empty, both open. Find: hours to fill.

Step 2: Sense check BEFORE any math. The drain is fighting the inlet, so the tank has to take LONGER than 4 hours to fill. Choice A is gone already.

Step 3: Pick a job size. 4 and 6 both divide into 12, so the tank holds 12 units.

Step 4: One hour of work. The inlet adds 12 ÷ 4 = 3 units per hour. The drain removes 12 ÷ 6 = 2 units per hour. Net gain: 3 minus 2 = 1 unit per hour.

Step 5: Finish it. At 1 unit per hour, 12 units take 12 hours. The answer is D.

Check it. In 12 hours the inlet adds 12 × 3 = 36 units and the drain removes 12 × 2 = 24 units. 36 minus 24 = 12 units. Full tank.

The trap. Plug 4 and 6 into the "together" formula and you get (4 × 4 ... no, (4 × 6) ÷ (4 + 6) = 24 ÷ 10 = 2.4 hours. That's choice A, and it treats the drain like a second inlet. A Test Taker who just adds the two times gets 10, which is choice C. Both come from grabbing a tool before thinking about what's actually happening in the tank.

Stop for a second and look at what you just did. Two different twists. Zero new formulas. The same question both times: how much gets done in one hour?

A water tank with a thick stream pouring in at the top and a thinner stream leaking out at the bottom, the water level rising slowly. — When something works against you, subtract its share each hour.

The mistakes I see every week (and what to do INSTEAD)

Writing the formula before you've read the whole prompt. The twist is usually in the last line.
INSTEAD: Read to the end. On your pad, write who works, for how long, and what changes and when. Then start the math.
Juggling fractions like 1/6 + 1/4 in your head. That's where the silly mistakes live.
INSTEAD: Pick a job size that every time divides into, and write each rate as a whole number on paper.
Skipping the sense check.
INSTEAD: Before doing any math, ask whether the answer should be bigger or smaller than each worker alone. Two helpers together must beat the fastest one alone. A drain must make the job slower. That one question kills wrong answers for free.
Memorizing a separate formula for every version. A leak formula, a three worker formula, a "people and days" formula. That's a lot of clutter to carry into a timed section.
INSTEAD: Use the one question for all of them. Say 5 painters can paint a house in 8 days. Then the job is 5 × 8 = 40 "painter days" of work. How long for 4 painters? 40 ÷ 4 = 10 days. Same logic, no new formula.
Thinking "I'm good at math, I don't need to write this down." That's pride, and it's a ceiling.
INSTEAD: Write every rate and every chunk of work. Notes cost you seconds. Re-reading a prompt and redoing math in your head costs you minutes and points.

If you've spent years telling yourself you're "bad at math," this should be a relief. You don't need a better memory. You need a better process, and you can still rock your GMAT without being a math person at all.

Your challenge for today

Pull out five work rate questions you've ALREADY answered, ideally from the official practice materials. Redo every one of them on paper with no formula allowed. For each, pick a job size, write each worker's rate per hour as a whole number, and do a sense check before the math. Then write one short line naming the twist in that question.

I'll bet at least one of those five is a question you originally got right the long way, or got wrong because the formula fed you a trap answer. Find it. Redo it until the new way feels automatic. That's not studying. That's training.