GRE Quant · Study & Practice

Rates, Work & Speed

AreaArithmetic DifficultyMedium GRE weightageHigh — rate and work word problems appear on nearly every GRE, and the same logic drives Data Interpretation

Almost every "rate" question on the GRE — miles per hour, jobs per day, dollars per pound, litres per minute — is the same relationship in different clothing: rate × time = amount. Get comfortable rearranging that one equation and the whole chapter opens up. The two ideas that trip people up are averages and teamwork. An average speed is never the plain average of two speeds when the times differ — it is total distance over total time, which is why a there-and-back trip at 40 and 60 does not average 50. And when two people or machines work together, you add their rates, not their times. The GRE keeps the numbers clean because the on-screen calculator is basic and slow, so the winning move is almost always to set up the right relationship and reason, not to grind. This chapter covers unit rates and conversions, the average-rate trap, the speed–distance–time triangle, and combined work — each with the fast method and the traps that quietly cost points.

Topics

1 Unit Rates & Unit Conversion 4 worked · 5 practice · 8-Q test Start → 2 Average Rate 4 worked · 5 practice · 8-Q test Start → 3 Speed, Distance & Time 4 worked · 5 practice · 8-Q test Start → 4 Combined Work 4 worked · 5 practice · 8-Q test Start →

⚡ GRE shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Everything is rate × time = amount. Write down which two you know and solve for the third — do not memorise separate formulas.
  • Average speed = total distance ÷ total time. The plain average of two speeds is right only when the times are equal.
  • Equal distances at speeds a and b ⇒ average speed = 2ab/(a + b) (the harmonic mean), always less than the plain average.
  • km/h ÷ 3.6 = m/s, and m/s × 3.6 = km/h. Memorise this one conversion; it appears constantly.
  • Work problems: add rates, not times. Two workers of times a and b together take ab/(a + b).
  • Toward each other ⇒ add speeds; chasing ⇒ subtract speeds. Then time = gap ÷ relative speed.

⚠️ Common mistakes & traps

GRE is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • Averaging two speeds when the distances (not the times) are equal — you must use total distance over total time.
  • Mixing units: multiplying a km/h speed by a time left in minutes. Convert first.
  • Averaging times in a work problem instead of adding rates (a helper must reduce the time below either worker’s).
  • Forgetting to subtract a drain’s or headwind’s rate that works against the main rate.
  • In relative-speed problems, adding when you should subtract (catch-up) or vice versa (approach).
  • Adding the train length to nothing when it crosses a bridge — distance is train length PLUS bridge length.

📈 GRE exam insight & question patterns

Quantitative Comparison — a round trip covers equal distances at 30 and 60 km/h. Quantity A: average speed. Quantity B: 45 km/h. Which is greater?

Quantity B. Equal distances ⇒ average = 2·30·60/90 = 40 km/h < 45. The tempting "45" is the plain-average trap.

Work — machine P does a job in 6 hours, machine Q in 3 hours. How long together?

Rates 1/6 + 1/3 = 1/2, so together 2 hours. (Or 6·3/9 = 2.)

Numeric Entry — a car travels 165 km in 2 hours 45 minutes. Enter its average speed in km/h.

2 h 45 min = 2.75 h; 165/2.75 = 60 km/h.

Relative speed — two runners on a 400 m track start together and run in opposite directions at 5 and 3 m/s. When do they first meet?

Combined 8 m/s over 400 m ⇒ 400/8 = 50 seconds.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

Core rate equationTap to reveal
rate × time = amount (distance, work, cost)
Average speedTap to reveal
total distance ÷ total time (not the average of speeds)
Equal distances at a and bTap to reveal
average = 2ab/(a + b) (harmonic mean)
km/h to m/sTap to reveal
divide by 3.6
Combined work of times a, bTap to reveal
together = ab/(a + b); or add 1/a + 1/b
Approaching vs chasingTap to reveal
add speeds (approach) / subtract speeds (chase)
Train crossing a bridgeTap to reveal
distance = train length + bridge length
Tap filling with a leakTap to reveal
net rate = fill rate − drain rate

📌 Quick revision

Every rate question is rate × time = amount in disguise, so identify the two quantities you know and solve for the third. Average speed is total distance over total time — the plain average of two speeds is a trap unless the times are equal, and for equal distances the answer is the harmonic mean 2ab/(a + b). In work problems, add rates rather than times: two workers of times a and b together take ab/(a + b), and a drain or headwind subtracts its rate. For moving objects, add speeds when they approach and subtract when one chases the other. Keep units consistent, remember km/h ÷ 3.6 = m/s, and the GRE’s deliberately clean numbers fall out without leaning on the basic calculator.

Chapter test

📝 Rates, Work & Speed — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
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🏆 Vidaara GRE success checklist

You have truly mastered Rates, Work & Speed when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (4 topics)4/4
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall8 cards