Rates and Distance: Build the TABLE Before You Touch an Equation

By EMPOWERgmat on March 4, 2025

Here is a scene I watch every single week. Someone reads a rate question, sees two speeds and a total time, and starts writing an equation on the very first line of their notepad. Halfway through, they realize they paired the wrong time with the wrong speed. They cross it out. They re-read the prompt. They start again. Three minutes later they pick the answer that 'looks right.' It's wrong.

Here's my verdict: rate questions are NOT hard. They are MESSY. You get two or three speeds, a couple of times, a distance or two, and a story wrapped around all of it. The math underneath is almost always simple. What breaks people is the sorting. And the fix for a sorting problem is not more algebra. It's a table.

The clock makes messy expensive

On the GMAT Focus Edition, the Quantitative Reasoning section gives you 21 questions in 45 minutes, and every one of them is Problem Solving: a question with five answer choices, and you pick one. You can check the format on GMAC's official page about the exam. That works out to a little over 2 minutes per question on average. A rate question that you start twice eats the time of two questions. A rate question you start twice AND get wrong is a disaster.

So I'll make you a wager. Go back to the last rate question you missed. I'll bet the math wasn't the problem. I'll bet you either mixed up which number belonged to which part of the trip, or you never wrote the pieces down at all.

The table

Every rate question runs on one relationship: Rate × Time = Distance. Rate just means speed, like miles per hour. That's it. That's the whole formula.

The table is how you stop the numbers from wandering. Draw three columns: Rate, Time, Distance. Then give one row to each mover, or to each leg of a trip. Every row has to obey Rate × Time = Distance on its own. Then you fill it in like this:

Put in every number the prompt gives you, in the row it belongs to. Write the units.
Pick ONE unknown and call it a letter. Then write every other blank in terms of that letter.
Find the link between the rows. Same distance? Distances add up to a total? Times add up to a total? The prompt always tells you. That link IS your equation.

Stop reading for a second and notice what just happened. You never had to 'think up' an equation. The table handed it to you.

A hand-drawn grid on a notepad with three columns and two rows, each box neatly filled, next to a crumpled sheet covered in scribbled crossed-out work. — Same question, two notepads. One of them gets it right on the first try.

Try it on a round trip

Try it

Dana drives from Town A to Town B at an average speed of 60 miles per hour. She returns along the same road at an average speed of 40 miles per hour. The whole round trip takes 5 hours. How many miles is it from Town A to Town B?

Show the answer

Step 1: build the table. Two legs, so two rows. The link between them: the distance is the SAME both ways, and the times add up to 5.

Leg	Rate	Time	Distance
Going	60	t	60t
Return	40	5 − t	40(5 − t)

Step 2: set the distances equal. 60t = 40(5 − t), so 60t = 200 − 40t, so 100t = 200, so t = 2. The one way distance is 60 × 2 = 120.

Step 3: check it. 120 miles at 60 mph is 2 hours. 120 miles at 40 mph is 3 hours. 2 + 3 = 5. It works. The answer is (B).

The cheap way: TEST THE ANSWERS. Start with (B), 120. Divide by each speed: 2 hours plus 3 hours is 5 hours. Done in about twenty seconds.

The trap: averaging the speeds. People think 'the average of 60 and 40 is 50, so 50 × 5 = 250 miles total, half of that is 125.' That's (C), and it's wrong. She spends MORE time at the slower speed, so her average speed is below 50. Test it: 125 miles takes about 2.08 hours at 60 and 3.125 hours at 40, which is more than 5 hours. And (E), 240, is the round trip distance, sitting there for anyone who answers the wrong question.

Notice which way was faster. The algebra was fine. Testing the answers was faster. The prompt gave you five numbers to try, and the GMAT is not going to take points off for using them. If you want the full argument for that habit, read why every Quant question is Problem Solving now and why you should TEST THE ANSWERS. But even when you test the answers, the table tells you WHAT to test and in which order.

Try it on a head start

Try it

Two cyclists start 100 miles apart and ride toward each other on the same road. The first cyclist rides at 10 miles per hour and leaves 1 hour before the second. The second cyclist rides at 20 miles per hour. When they meet, how many miles has the second cyclist ridden?

40
50
60
66 2/3
70

Show the answer

Step 1: build the table. Let t be the time the SECOND cyclist rides. The first cyclist rides 1 hour longer. The link: they ride toward each other, so their distances add up to 100.

Rider	Rate	Time	Distance
First	10	t + 1	10(t + 1)
Second	20	t	20t

Step 2: add the distances. 10(t + 1) + 20t = 100, so 10t + 10 + 20t = 100, so 30t = 90, so t = 3. The second cyclist rides 20 × 3 = 60 miles.

Step 3: check it. The first cyclist rides 4 hours at 10 mph, which is 40 miles. 40 + 60 = 100. The answer is (C).

The trap: ignoring the head start. If you just say 'they close the gap at 30 mph, so 100 ÷ 30 = 3 1/3 hours,' then the second cyclist rides 20 × 3 1/3 = 66 2/3 miles. That's (D), and it's sitting there waiting for you. And (A), 40, is the FIRST cyclist's distance, waiting for anyone who answers about the wrong person. The table puts 't + 1' in a box, right where you can see it, so the head start can't slip away.

Two cyclists on a long straight road riding toward each other, one already a short way down the road while the other is just pushing off. — The head start is the whole question. Give it its own box.

5 mistakes I see on rate questions

Writing the equation first. You read, you panic, you write '60t = 40t' and hope. INSTEAD: draw the three columns before you write a single equation. The equation comes LAST.
Averaging the speeds. Going 60 one way and 40 back does not average to 50. INSTEAD: give each leg its own row and let the times do the work.
Mixing minutes and hours. The prompt says 30 minutes and the speed is in miles per hour, and suddenly someone is multiplying 30 by 20. INSTEAD: convert in the table and write the unit in every box. 30 minutes goes in as 1/2 hour.
Doing it in your head. 'I'm good at math, I don't need a table.' That's pride talking, and pride is the most expensive habit on this test. INSTEAD: write it down every time, especially on the 'easy' ones, because those are the points you can't afford to drop.
Answering the wrong question. You solved for t and the question asked for distance. Or you found the first rider's distance and it asked about the second. INSTEAD: before you build the table, write what they're asking for at the top of your notes and circle it.

It's bigger than trains and cyclists

The same table handles work questions too. Swap Distance for 'Work done' and the rate becomes 'jobs per hour.' A pipe filling a tank, two printers splitting an order, a painter who quits halfway: same three columns, same rule across every row, same link between rows. Learn ONE tool well and it covers a whole family of questions. That's what training looks like. You're not memorizing a hundred tricks for a hundred stories. You're running the same play until it's automatic.

So you have to decide what you want MORE: to feel clever by solving it in your head, or to get the question right in under two minutes. You can't always have both.

Your challenge for today

Pull five rate or work questions you've already done, including at least two you got wrong. Redo every one with the table, on paper, with a timer running. Then compare. I'll bet at least one of the ones you missed was a sorting mistake, not a math mistake, and I'll bet the table made it obvious. Find it. Write down what the mistake was. That's one fewer point you give away on Test Day.

Sources

GMAC: About the GMAT exam (sections, timing and format)