# GMAT Prep – Rate Problems

by March 12, 2014

onRate problems are very prevalent on the Quantitative section of the GMAT exam. They are also present in Data Sufficiency and Problem Solving as well, but to a lesser extent. The majority of rate problems require solid proficiency in ratio concepts and knowledge of the two primary rate formulae:

Speed Formula: time x speed = distance

Productive Work Formula: time x rate = units produced

Which formula you use has everything to do with the question. You will also need to adjust the formula accordingly. Rate problems are, by definition, word problems; so being able to translate the information in the question into mathematical form is essential.

Let’s try a practice question:

Two buses, A and B, started simultaneously from opposite ends of the same 50-mile bus route and traveled toward each other, making their regular trips. Bus A, traveling at a constant rate, completed the 50-mile trip in 2 hours; Bus B, traveling at a constant rate, completed the 50-mile trip in 1 hour. How many miles had Bus A traveled when it met Bus B?

From this information, we can determine the speed of the two buses easily:

Bus A – 50 miles/2 hrs = 25 miles/hr

Bus B – 50 miles/1 hr = 50 miles/hr

The ratio of the Bus A to Bus B is 2:1.

Now, adjust the rate formula so that “time” is the amount of time passed when the buses meet. Bus A will have traveled 25(time) and Bus B will have traveled 50(time). Logically, something may occur to you right away – the entire length of the route has been covered, by either Bus A or Bus B. That means, together, at their time of meeting, the combined distance of the two buses is 50 miles. Now, set up your equation again.

25(time) + 50(time) = 50 miles

Combine like terms: 75(time) = 50 miles

time = 2/3 hour (or 40 minutes, but do not change units halfway through a question!)

Now, to figure out the distance covered by Bus A, plug the time and speed into our formula again:

2/3 hour x 25 miles/hr = 16 2/3 miles.

The exceptional flexibility of this formula is what makes it so useful, but this can also make a rate problem much trickier than the word problems you may remember from your pre-college days. This question requires you to know that you can use combined rates without changing the formula’s format. Practice makes perfect, so try out some rate questions in your Official Guide to the GMAT and Official Guide to the GMAT Quantitative Review.

## Official Guide to the GMAT

**Problem Solving**: q19 p154, q25 p155, q28 p155, q31 p156, q82 p162, q87 p163, q90 p163, q103 p165, q126 p16, q154 p173, q185 p177, q223 p182

** Data Sufficiency**: q19 p279, q33 p280, q79 p284, q81 p284

## Official Guide to the GMAT Quantitative Review

** Problem Solving**: q14 p63, q21 p64, q52 p68 (Mixture), q69 p70, q79 p71, q87 p73, q91 p73, q119 p77, q130 p78, q131 p79 (Mixture), q136 p79, q140 p80

**Data Sufficiency**: q31 p151, q38 p152, q47 p152, q54 p153, q69 p154

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