You set the expression for Roger's distance from home equal to the expression for Bill's distance from home. Solve the equation to find the value of x, or the time in hours when they are the same distance away from home.

Question

Roger's distance from home = Bill's distance from home
70−5x
=
10+15x

x
=

Answer 1

To find the value of \( x \) where Roger's distance from home equals Bill's distance from home, we start with the equation:

\[ 70 - 5x = 10 + 15x \]

Now, we'll solve for \( x \) step by step.

1. Add \( 5x \) to both sides:

\[ 70 = 10 + 15x + 5x \]

2. Combine like terms:

\[ 70 = 10 + 20x \]

3. Subtract 10 from both sides:

\[ 70 - 10 = 20x \]

\[ 60 = 20x \]

4. Divide both sides by 20:

\[ x = \frac{60}{20} \]

\[ x = 3 \]

Thus, the value of \( x \), or the time in hours when Roger and Bill are the same distance away from home, is

\[ \boxed{3} \]