Question

3 - 10. ac is a straight segment as shown in the diagram below. if the distance between points a and c is 67 miles, determine the distance between points a and b.
a 5x - 2 b 2x + 6 c

Explanation:

Step1: Set up an equation

Since $AC = AB + BC$ and $AC = 67$, $AB=5x - 2$, $BC = 2x+6$, we have the equation $(5x - 2)+(2x + 6)=67$.

Step2: Simplify the left - hand side of the equation

Combining like terms, $5x+2x-2 + 6=67$, which simplifies to $7x+4 = 67$.

Step3: Solve for $x$

Subtract 4 from both sides: $7x=67 - 4$, so $7x=63$. Then divide both sides by 7: $x=\frac{63}{7}=9$.

Step4: Find the distance between $A$ and $B$

Substitute $x = 9$ into the expression for $AB$: $AB=5x-2=5\times9-2=45 - 2=43$.

Answer:

43 miles