Solving Distance Problems

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Solving distance problems is an important skill to have for the CSET Multiple Subjects exam. Distance problems usually form a geometric shape when you draw the diagram. Once you recognize the geometric shape, you then apply the appropriate formula to solve.

In this lesson we will solve two distance problems. We will then watch a video on the more advanced distance, rate, and time problem. Please note that due to .html limitations, we will be using the radical sign √ to mean the “square root” of.

Problem 1

A woman starts at home, jogs 4 miles east, and then 5 miles northwest. How far is she from home?

Step 1:
Draw a diagram of the problem:

Step 2:
Setup the equation a² + b² = c²
Notice that both a and b are on the same side of the equation so which side you choose as “a” and which side you choose as “b” is not important. What is important is that side “c” (the hypotenuse) is correct. In this case, side c is 5. So we set our equation as:
4² + b² = 5²

Step 3:
Now solve:
4² + b² = 5²
16 + b² = 25
-16          -16
b² = 9
b = √9
b = 3
So she is 3 miles from home.

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