GMAT Ratios, Rates and Work Problems

By Muntasir Aug 04, 2026 8 min read

TL;DR

Ratio, rate and work problems run through the GMAT Quant Reasoning section, which has 21 Problem Solving questions in 45 minutes and no calculator allowed. Treat every ratio number as a part: a 3 to 5 ratio means the real values are 3x and 5x for some number x, not 3 and 5 themselves.

For rate problems, distance equals rate multiplied by time (d = rt), and average speed equals total distance divided by total time, never the plain average of two speeds. For combined work, add individual rates together: 1/A + 1/B equals 1 divided by the combined time. For two objects moving toward each other, add the speeds. For a same-direction chase, subtract them.

Ratio, rate and work problems appear across the GMAT Quant Reasoning section, wherever the exam asks you to compare quantities, calculate speed or timing, or combine two workers' output. The section is composed of 21 Problem Solving questions, and Quantitative Reasoning runs 45 minutes. Data Sufficiency does not appear in the GMAT Focus Edition's Quant section, since mba.com lists it under Data Insights. No calculator is allowed during Quant Reasoning, and mba.com states the section measures arithmetic and algebra foundational knowledge, where success depends on logic and analytical skills, not advanced math.

This guide covers setting up ratios and proportions without error, applying the distance equals rate times time formula, combining work rates for two or more workers, and handling relative-speed problems where two objects move toward or away from each other. Each section states the setup rule first, then runs a number through it. Four full walkthroughs at the end show every pattern solved step by step.

Setting Up Ratios and Proportions Correctly

A ratio compares two or more quantities using a shared multiplier, often called a part. Writing a ratio as 3 to 5 does not mean the actual values are 3 and 5. It means the values are 3x and 5x for some positive number x, and finding x from the given total or difference solves the problem.

Ratios as Parts, Not Actual Values

Treat every number in a ratio as a part, not a finished value. If a bag holds marbles in a ratio of red to blue of 2 to 3, and the bag holds 25 marbles total, the parts add to 2 plus 3, or 5. Each part equals 25 divided by 5, or 5 marbles. Red marbles equal 2 times 5, or 10, and blue marbles equal 3 times 5, or 15.

Cross-Multiplying to Solve Proportions

A proportion sets two ratios equal to each other, written as a/b = c/d. Cross-multiplying gives ad = bc, and solving for the unknown value follows standard algebra rules. Setting 3/4 equal to x/20 gives 4x = 60, so x equals 15.

Follow these steps to set up and solve a proportion cleanly.

Write both ratios as fractions with matching units on top and matching units on bottom.
Cross-multiply, the numerator of one side times the denominator of the other.
Set the two products equal and solve for the unknown.
Check the direction of the answer, a larger part should give a larger actual value.

Common Ratio Traps

A few setup mistakes account for most ratio errors on test day.

Treating a part-to-part ratio, such as red to blue, as a part-to-whole ratio, red to total.
Adding or subtracting ratio numbers directly instead of scaling both sides by the same factor.
Mixing units inside one ratio, such as feet on one side and inches on the other.
Assuming an old ratio still applies after the problem states a new ratio takes over.

The Rate-Distance-Time Formula and Its Traps

Every rate-distance-time problem reduces to one formula: distance equals rate multiplied by time, written d = rt. Rearranged, rate equals distance divided by time (r = d/t), and time equals distance divided by rate (t = d/r). A car covering 150 miles at 50 mph takes 150 divided by 50, or 3 hours.

Converting Units Before You Calculate

Rate problems mix units on purpose, minutes with hours, or feet with miles. Convert every value to matching units before plugging into d = rt. A speed given in miles per hour paired with a time in minutes produces a wrong answer unless the minutes convert to hours first, for example 30 minutes converts to 0.5 hours. Convert the result back if the question asks for minutes, so 1.5 hours becomes 90 minutes.

Average Speed Is Not the Average of Two Speeds

Average speed equals total distance divided by total time, not the arithmetic mean of two speeds. A trip covering 60 miles at 30 mph, then another 60 miles at 60 mph, takes 2 hours plus 1 hour, for 3 hours total across 120 miles. Average speed equals 120 divided by 3, or 40 mph, not the 45 mph mean of 30 and 60.

Combined Work-Rate Problems

Work-rate problems treat a full job as one unit of work, and set each worker's rate as 1 divided by the time the worker takes working alone. A worker completing a job in 6 hours works at a rate of 1/6 of the job per hour. Rates written this way add and subtract cleanly, while raw completion times do not.

The table below shows two workers set up this way before combining their rates.

Worker	Time Alone (hours)	Rate (job per hour)
Painter A	6	1/6
Painter B	4	1/4

Individual Rates Add When Working Together

Two workers operating at the same time add their rates: 1/A + 1/B = 1/T, where T equals the combined time. Painter A at 1/6 of the job per hour and Painter B at 1/4 of the job per hour combine to 1/6 + 1/4, or 5/12 of the job per hour. Combined time equals the reciprocal of the combined rate, 12/5, or 2.4 hours.

Rates Subtract When Working Against Each Other

A drain, a leak, or a second process working in the opposite direction subtracts from the combined rate instead of adding. A pipe filling a pool at 1/5 of the pool per hour, paired with a drain emptying it at 1/8 of the pool per hour, produces a net rate of 1/5 minus 1/8, or 3/40 of the pool per hour. Filling the pool then takes the reciprocal of 3/40, or 40/3 hours, roughly 13.3 hours.

Relative-Speed and Opposite-Direction Setups

Two moving objects combine their speeds differently depending on the direction of travel.

Setup	Combined Speed	What It Finds
Moving toward each other	Speed A + Speed B	Time until the two meet
Moving in the same direction (catch-up)	Faster speed minus slower speed	Time until the faster one catches up

Opposite Directions: Add the Speeds

Two objects starting apart and moving toward each other close the gap at a combined speed equal to the sum of their individual speeds. Dividing the starting distance by the combined speed gives the time until they meet. Two cars 240 miles apart, one at 40 mph and one at 60 mph, close at 100 mph and meet after 2.4 hours.

Same Direction: Catch-Up Problems Subtract the Speeds

When one object chases another moving the same direction, the gap closes at a rate equal to the faster speed minus the slower speed. Dividing the starting gap by this difference gives the time needed to catch up. A runner 2 miles ahead at 6 mph, chased at 8 mph, loses the lead after 2 divided by 2, or 1 hour.

Sample Problem Walkthroughs

The four walkthroughs below apply the rules above to full problems, worked step by step.

Ratio Word Problem

Question: A club has members in a ratio of boys to girls of 7 to 5. The club has 96 members total. How many girls belong to the club?

Solution: The ratio parts add to 7 plus 5, or 12. Each part equals 96 divided by 12, or 8 members. Girls equal 5 parts, so 5 times 8 equals 40 girls.

Rate-Distance-Time Word Problem

Question: A cyclist rides 60 miles at a constant speed, then returns along the same route at a speed 5 mph slower. The return trip takes 1 hour longer than the trip out. What speed did the cyclist ride on the way out?

Solution: Let r equal the outbound speed in mph. Time out equals 60/r, and time back equals 60 divided by (r minus 5). The return trip takes 1 hour longer, so 60 divided by (r minus 5), minus 60/r, equals 1. Multiplying through by r(r minus 5) gives 60r minus 60(r minus 5) equals r(r minus 5), which simplifies to 300 equals r squared minus 5r. Solving the quadratic r squared minus 5r minus 300 equals 0 gives r equals 20, since the negative root is rejected, speed must be positive. The cyclist rode 20 mph on the way out.

Combined Work-Rate Word Problem

Question: Machine A fills a tank in 6 hours working alone. Machine B fills the same tank in 4 hours working alone. Working together, how long do the two machines take to fill the tank?

Solution: Machine A's rate equals 1/6 of the tank per hour, and Machine B's rate equals 1/4 of the tank per hour. Combined rate equals 1/6 + 1/4, or 5/12 of the tank per hour. Combined time equals the reciprocal, 12/5 hours, or 2.4 hours.

Relative-Speed Word Problem

Question: Two trains start 300 miles apart and travel toward each other, one at 50 mph and the other at 70 mph. Both speeds stay constant for the whole trip. How long until the trains meet?

Solution: Since the trains move toward each other, their speeds add: 50 plus 70 equals 120 mph combined. Time to close a 300-mile gap at 120 mph equals 300 divided by 120, or 2.5 hours. Check the split: the 50 mph train covers 125 miles and the 70 mph train covers 175 miles, adding to 300.

Practice these skills with our free Ratio & Proportion and Rate, Distance & Work drills, each offering three difficulty levels with instant scoring and no signup required. For the full Quant Reasoning breakdown, read our GMAT Quant Reasoning guide, and for ratio logic applied to mixtures and interest, see mixtures, interest and profit. Visit our GMAT prep page for the full library of mocks and section practice, or check your target score with our GMAT score calculator.