HANDLING MATHEMATICAL CALCULATIONS AND WORD PROBLEMS

Do you remember solving word problems in high school algebra class? If you found these types of problems difficult to solve, it was probably because you didn't know exactly what information you were required to calculate. One of the keys to deciphering word problems is to look for key phrases and apply the appropriate formula:

 If the question asks: You are asked to find: Use formula: How fast? speed distance/time How long does it take? time distance/speed How far? distance speed X time

Understanding & Calculating Lag Time

Compare the relative speeds of 2 vehicles, A and B. Both vehicles leave the same departure point but travel at different speeds. Vehicle A is traveling at 50 miles/hour. Vehicle B is traveling 25 miles/hour. Assuming that neither vehicles slow down nor stop, how long does it take for each to travel 250 miles? Before you blurt out the answer, try using one of the above three formulas. Which is the correct formula to apply here? If you chose the "time" formula, you're right. (Why? The key phrase in the word problem is "how long does it take"). So, if you take the distance, 250 miles; and divide by the speed of each vehicle, you should get:

 Car A Car B distance = 250 miles speed = 50 miles/hr. Time = Distance / Speed =  250 miles/(50 miles/hour) = 5 hours distance = 250 miles speed = 25 miles/hr. Time = Distance / Speed 250 miles/(25 miles/hr) = 10 hours

So, the lag time difference between the two vehicles (10 hours - 5 hours) is 5 hours. What would the lag time be if the distance traveled were 500 miles?

Vehicle A would take 10 hours to travel 500 miles, but Vehicle B would take 20 hours. The lag time here is 10 hours. So, the pattern you should note here is "the greater the distance, the longer the lag time."

The same method of calculation may be used for earthquake waves (P-waves and S-waves). However, you must use consistent units. If you are given speed units which are "miles per second," you must not mix them with "miles per hour."

The central assumption for using this methodology for calculating the distance to the earthquake epicenter is that the speed of the earthquake waves does not change with distance. However, in reality, this does not hold true over long distances, especially if the earthquake waves penetrate the denser layers of the earth's interior, which causes earthquake waves to speed up in general.

At least 3 earthquake recording stations are required to find the location of the earthquake epicenter. A single recording station can only calculate distance, but not direction; to cover all possibilities, a complete circle is drawn around that station.