Imagine you are traveling from City A to City B. After your journey, you want to find out the average speed of the entire journey. Suppose, you were at a speed of 60 miles per hour on the freeway and 30 miles per hour in the city. What would be your average speed in this scenario?
Average speed is a commonly tested area in the GMAT. Many test takers, faced with a problem like above, would simply average these two speeds and come up with 45 miles per hour as the answer. Absolutely wrong! Since you drove at both these speeds in different time, your answer needs to factor in that element. So, if you spent more time on the freeway driving at 60 miles per hour, your answer would be closer to this figure.
You know that speed is defined as distance divided by time. Similarly, average speed is nothing but total distance divided by total time. Remember this cardinal rule.
Also, the folks at GMAC know about this well and would trick you with the average of the two speeds (45 in this case) as one of the answer choices. Do not fall for the trap. You need to have information on the distance travelled and time taken as well. If there is limited information available, you need to be more careful about the answer.
However, you can average the two speeds in one special condition. If the time taken for two speeds is the same, then the average of the two speeds will give you the correct answer. For instance, if you drove two hours at 60 miles per hour and then two hours at 30 miles per hour, the correct average speed in this case would indeed be 45 miles per hour.
In some problems, you may not be given the distance and time variables. In such a case, you need to plug a number for the distance, calculate the time based on that distance and then calculate the average speed.
When solving average speed problems, keep in mind that the units of measurement should be the same. While it is a basic concept, sometimes test takers falter on the day of the exam. With different units, you will always arrive at the wrong answer even with the correct formula.
There is a shortcut you can employ if the distance travelled is the same. For eg, if you drove from City A to City B at 40 miles per hour and came back from City B to City A at 60 miles per hour, then the average speed would be twice the product of the speeds divided by the sum of the speeds. In this case it would be:
2x40x60\40+60 which is 4800\100 which gives the answer as 48 miles per hour.
If you are unsure you can go back to the general formula of average speed which is total distance divided by total time. Also, if you are using the shortcut, you can use the general formula to verify your answers.