"At the Rate of M Meters per S Seconds..." — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

At the rate of $m$ meters per $s$ seconds, how many meters does a cyclist travel in $x$ minutes?

(A) $\dfrac{m}{sx}$

(B) $\dfrac{mx}{s}$

(C) $\dfrac{60m}{xs}$

(D) $\dfrac{60ms}{x}$

(E) $\dfrac{60mx}{s}$

Try it before reading on.

Step 1: Write Down What Each Variable Represents

When a word problem gives you variables that represent real-world quantities, write down what each one means. This takes a few seconds and prevents the most common kind of error — mixing up which variable goes where.

• $m$ = meters
• $s$ = seconds
• $x$ = minutes (the time the cyclist travels)

Also note the rate: the word "per" means "divided by." So "$m$ meters per $s$ seconds" gives us a rate of $\frac{m}{s}$ meters per second.

If "per" as "divided by" is new to you, make a note to memorize it. The word before "per" goes in the numerator. The word after "per" goes in the denominator. This comes up constantly on the GMAT®.

Step 2: Set Up the Rate Chart

When a problem uses the word "rate," write the formula $R \times T = D$ across the top of your scratch work and fill in the columns.

Here's the chart with what the problem gives us:

The distance column is empty because that's what we're solving for.

Step 3: Convert Units

There's a mismatch. The rate is in seconds. The time is in minutes. We need a common unit before multiplying.

It's easier to convert $x$ minutes to seconds than to convert $\frac{m}{s}$ to minutes, because $x$ is a single term and $\frac{m}{s}$ has two. Converting the simpler side means less chance for error.

Write the conversion as a fraction with the unit you want on top and the unit you want to cancel on the bottom:

$x \text{ minutes} \times \frac{60 \text{ seconds}}{1 \text{ minute}} = 60x \text{ seconds}$

The minutes cancel. We're left with seconds.

Now update the chart:

Step 4: Multiply Rate × Time to Get Distance

$\text{Distance} = \frac{m}{s} \times 60x = \frac{60mx}{s}$

The seconds unit cancels. We're left with meters — which is what the question asks for.

The answer is (E).

Why This Problem Matters

About 20% of test takers miss this problem. The wrong answers distribute across (B), (C), and (D) — and each one maps to a specific, predictable mistake.

Choosing (B) — $\frac{mx}{s}$: you set up the rate chart correctly and multiplied right, but forgot to convert $x$ minutes to seconds. The 60 is missing. This is the most common version of the error: the algebra is right, the units are wrong.

Choosing (C) — $\frac{60m}{xs}$: you remembered the 60 but put $x$ in the denominator instead of the numerator. The 60 converted the units, but the variable placement got flipped — likely from setting up the fraction upside down during the conversion step.

Choosing (D) — $\frac{60ms}{x}$: you remembered the 60 but put $s$ in the numerator and $x$ in the denominator. The rate fraction $\frac{m}{s}$ got inverted to $\frac{s}{m}$, or the conversion fraction was written backwards.

All three wrong answers come from organizational errors, not knowledge gaps. The math isn't hard. The setup is where it breaks down.

That's why the rate chart matters. Writing the units in every cell makes the seconds-vs-minutes mismatch visible before you start computing. Without the chart, the mismatch is easy to miss — you're just multiplying variables, and nothing signals that the units don't align.

The rate chart doesn't solve the problem for you. It creates the conditions where you're less likely to make the mistake in the first place.

Want the full strategy behind this problem? Read: GMAT® Word Translations: The Step-By-Step Setup System

From Episode 25 of Real GMAT® Problems (The GMAT® Strategy Podcast).