1. **State the problem:** Two dogs start running toward a ball from different distances and speeds. We want to find the time when both dogs are the same distance from the ball. 2. **Define variables:** Let $t$ be the time in seconds after they start running. 3. **Write expressions for distances from the ball:** - Jack Russell terrier starts 90 meters away and runs at 11 m/s, so its distance from the ball after time $t$ is: $$90 - 11t$$ - Greyhound starts 140 meters away and runs at 19 m/s, so its distance from the ball after time $t$ is: $$140 - 19t$$ 4. **Set distances equal to find when they are the same:** $$90 - 11t = 140 - 19t$$ 5. **Solve for $t$:** $$90 - 11t = 140 - 19t$$ Add $19t$ to both sides: $$90 - 11t + 19t = 140$$ $$90 + 8t = 140$$ Subtract 90 from both sides: $$8t = 140 - 90$$ $$8t = 50$$ Divide both sides by 8: $$t = \frac{50}{8}$$ Show cancellation: $$t = \frac{\cancel{50}^{\times 2 \times 25}}{\cancel{8}^{\times 2 \times 4}} = \frac{25}{4}$$ 6. **Convert to decimal if desired:** $$\frac{25}{4} = 6.25$$ seconds **Final answer:** The dogs are the same distance from the ball after **$\frac{25}{4}$ seconds** or **6.25 seconds**.