MathChat

How to Conquer Word Problems —

Easy, you just need to use “Master Equations.”

A “what?” you ask. A “Master Equation,” I reply.

That  is a template that helps you solve word problems in two key ways:

1)  It lets you know what kind of word problem you are dealing with in the first place — you’ll be able to categorize it, AND …

2)  It gives you a “blueprint” for solving the problem, providing a quick and direct path between the problem and the answer.

Let me give you examples of two Master Equations that can help you solve those oft-vexing rate-time-distance problems.

The first master equation, Master Equation “A” is:
Distance 1  =  Distance 2

This is the one to use for word-problem situations like these:

—  Mike bikes from home to the Slippery Rock Climbing Gym, then he  bikes back, from the gym to home.

—  Candace climbs up Pike’s Peak, then she runs down Pike’s Peak.

—  Little Alvin skateboards from his house to Tiny Ted’s house on Monday. On Tuesday he makes the same trip but on bicycle.

Notice that in all three of these situations the distance covered is the same. The distance from home to a gym is the same as the distance from the gym to home; the distance up a hill is the same as the distance down a hill. That’s what makes these all cases of Distance 1 = Distance 2. The first distance equals the second distance.

The second master equation, Master Equation “B” is:
Distance 1 + Distance 2  = Distance Total

This is the one for situations like these:

—  Mike bikes from home to the Slippery Rock Climbing Gym, then he  bikes a bit more, from the gym to Cheesman Park.

—  Candace and James are 400 miles apart. They drive toward each other furiously fast. When will their cars pass each other (assuming, hopefully, that they are in different lanes)?

—  Little Alvin and Tiny Ted stand back to back. Little Alvin walks east, and Tiny Ted walks west. When will they be seven miles apart?

Notice that in all of these situations there are two different distances, and the distances can be added together to give you a total distance. Mike first goes from his home to the gym, then from the gym to the park; Candace and James each drive separate distances, but together they go 400 miles. That is why you need to use the formula:  Distance 1 + Distance 2 =  Distance Total for these word problems.

So o.k., in this blog entry I am not going to explain how to use the “Master Equations” to finish solve the problems. If I did that, the entry would be too LONG.

But I will do this in my next blog.

Stay tuned!