Today’s GMAT tip comes from the folks at test prep firm Manhattan Review, who have some advice on how to handle rate problems on the GMAT:
Rate problems are very prevalent on the Quantitative section of the GMAT, particularly in Problem Solving, but to a lesser extent, Data Sufficiency as well. 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, and you will 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 also what can 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.
Read the full article: GMAT Tip: Solving Rate Problems
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