# GMAT Math: Rate Problems

Rate problems are very prevalent on the Quantitative section of the GMAT exam. 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 speed of Bus A to Bus B is 1:2.

### 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 both in the Problem Solving and Data Sufficiency sections in your Official Guide to the GMAT and Official Guide to the GMAT Quantitative Review.

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