You set the expression for Austin's distance from home equal to the expression for Lucas'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

You set the expression for Austin's distance from home equal to the expression for Lucas'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.
Austin's distance from home = Lucas's distance from home
70−5x
=
10+15x
 
x
=

GPT-4o mini · Answer

To solve the equation $70 - 5x = 10 + 15x$, we will first rearrange the equation to isolate $x$. 1. Start by adding $5x$ on both sides: $$ 70 = 10 + 15x + 5x $$ This simplifies to: $$ 70 = 10 + 20x $$ 2. Now, subtract $10$ from both sides: $$ 70 - 10 = 20x $$ Which simplifies to: $$ 60 = 20x $$ 3. Finally, divide both sides by $20$: $$ x = \frac{60}{20} = 3 $$ Thus, the value of $x$ is $3$. **Summary: $x = 3$ hours**.